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53,72*(x^3)+412,667*(x^2)-438,8=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
      3           2           
1343*x    412667*x    2194    
------- + --------- - ---- = 0
   25        1000      5
(1343x325+412667x21000)−21945=0\left(\frac{1343 x^{3}}{25} + \frac{412667 x^{2}}{1000}\right) - \frac{2194}{5} = 0
Simplificar
Teorema de Cardano-Vieta
reescribamos la ecuación
(1343x325+412667x21000)−21945=0\left(\frac{1343 x^{3}}{25} + \frac{412667 x^{2}}{1000}\right) - \frac{2194}{5} = 0
de
ax3+bx2+cx+d=0a x^{3} + b x^{2} + c x + d = 0
como ecuación cúbica reducida
x3+bx2a+cxa+da=0x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0
x3+412667x253720−109701343=0x^{3} + \frac{412667 x^{2}}{53720} - \frac{10970}{1343} = 0
px2+qx+v+x3=0p x^{2} + q x + v + x^{3} = 0
donde
p=bap = \frac{b}{a}
p=41266753720p = \frac{412667}{53720}
q=caq = \frac{c}{a}
q=0q = 0
v=dav = \frac{d}{a}
v=−109701343v = - \frac{10970}{1343}
Fórmulas de Cardano-Vieta
x1+x2+x3=−px_{1} + x_{2} + x_{3} = - p
x1x2+x1x3+x2x3=qx_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q
x1x2x3=vx_{1} x_{2} x_{3} = v
x1+x2+x3=−41266753720x_{1} + x_{2} + x_{3} = - \frac{412667}{53720}
x1x2+x1x3+x2x3=0x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0
x1x2x3=−109701343x_{1} x_{2} x_{3} = - \frac{10970}{1343}
Respuesta rápida [src] 
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                170294052889*re|------------------------------------------------------------------------|             /    /          _______________________\\     |  170294052889*im|------------------------------------------------------------------------|             /    /          _______________________\\                   /    /          _______________________\\|                   /    /          _______________________\\
                               |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||     |                 |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||                   |    |3223200*\/ 203144120309231113233 |||                   |    |3223200*\/ 203144120309231113233 ||
                               |/          ___\     /                           _______________________ |             |atan|---------------------------------||     |                 |/          ___\     /                           _______________________ |             |atan|---------------------------------||                   |atan|---------------------------------|||                   |atan|---------------------------------||
                               ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|     |                 ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|            ___    |    \        53179606409624963        /||            ___    |    \        53179606409624963        /|
                               ||- - - -------|*3 /   ----------------- + ----------------------------- |   412667*cos|---------------------------------------|     |                 ||- - - -------|*3 /   ----------------- + ----------------------------- |   412667*sin|---------------------------------------|   412667*\/ 3 *cos|---------------------------------------||   412667*\/ 3 *sin|---------------------------------------|
       412667                  \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /     |                 \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /                   \                   3                   /|                   \                   3                   /
x1 = - ------ - ----------------------------------------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- + ---------------------------------------------------------| - ---------------------------------------------------------
       161160                                           8657515200                                                                 322320                           \                                          8657515200                                                                 322320                                                   322320                         /                             322320
x1=−412667161160−4126673sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320−170294052889re⁡(1(−12−3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200+412667cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+i(−170294052889im⁡(1(−12−3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200+412667sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+4126673cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320)x_{1} = - \frac{412667}{161160} - \frac{412667 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + i \left(- \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320}\right) 
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                170294052889*re|------------------------------------------------------------------------|             /    /          _______________________\\     |  170294052889*im|------------------------------------------------------------------------|             /    /          _______________________\\                   /    /          _______________________\\|                   /    /          _______________________\\
                               |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||     |                 |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||                   |    |3223200*\/ 203144120309231113233 |||                   |    |3223200*\/ 203144120309231113233 ||
                               |/          ___\     /                           _______________________ |             |atan|---------------------------------||     |                 |/          ___\     /                           _______________________ |             |atan|---------------------------------||                   |atan|---------------------------------|||                   |atan|---------------------------------||
                               ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|     |                 ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|            ___    |    \        53179606409624963        /||            ___    |    \        53179606409624963        /|
                               ||- - + -------|*3 /   ----------------- + ----------------------------- |   412667*cos|---------------------------------------|     |                 ||- - + -------|*3 /   ----------------- + ----------------------------- |   412667*sin|---------------------------------------|   412667*\/ 3 *cos|---------------------------------------||   412667*\/ 3 *sin|---------------------------------------|
       412667                  \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /     |                 \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /                   \                   3                   /|                   \                   3                   /
x2 = - ------ - ----------------------------------------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- - ---------------------------------------------------------| + ---------------------------------------------------------
       161160                                           8657515200                                                                 322320                           \                                          8657515200                                                                 322320                                                   322320                         /                             322320
x2=−412667161160+4126673sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+412667cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320−170294052889re⁡(1(−12+3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200+i(−4126673cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+412667sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320−170294052889im⁡(1(−12+3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200)x_{2} = - \frac{412667}{161160} + \frac{412667 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + i \left(- \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200}\right) 
                                                                                           ___________________________________________________
                                                                                          /                           _______________________ 
                                                                                         /  53179606409624963   3*I*\/ 203144120309231113233  
                                                                                      3 /   ----------------- + ----------------------------- 
       412667                               170294052889                              \/     155027238848000              144291920           
x3 = - ------ - ------------------------------------------------------------------- - --------------------------------------------------------
       161160                   ___________________________________________________                              3                            
                               /                           _______________________                                                            
                              /  53179606409624963   3*I*\/ 203144120309231113233                                                             
                8657515200*3 /   ----------------- + -----------------------------                                                            
                           \/     155027238848000              144291920
x3=−412667161160−53179606409624963155027238848000+3203144120309231113233i14429192033−170294052889865751520053179606409624963155027238848000+3203144120309231113233i1442919203x_{3} = - \frac{412667}{161160} - \frac{\sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}{3} - \frac{170294052889}{8657515200 \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}} 
x3 = -412667/161160 - (53179606409624963/155027238848000 + 3*sqrt(203144120309231113233)*i/144291920)^(1/3)/3 - 170294052889/(8657515200*(53179606409624963/155027238848000 + 3*sqrt(203144120309231113233)*i/144291920)^(1/3))
Suma y producto de raíces [src] 
suma
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           170294052889*re|------------------------------------------------------------------------|             /    /          _______________________\\     |  170294052889*im|------------------------------------------------------------------------|             /    /          _______________________\\                   /    /          _______________________\\|                   /    /          _______________________\\              170294052889*re|------------------------------------------------------------------------|             /    /          _______________________\\     |  170294052889*im|------------------------------------------------------------------------|             /    /          _______________________\\                   /    /          _______________________\\|                   /    /          _______________________\\                                                                                                                                            
                          |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||     |                 |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||                   |    |3223200*\/ 203144120309231113233 |||                   |    |3223200*\/ 203144120309231113233 ||                             |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||     |                 |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||                   |    |3223200*\/ 203144120309231113233 |||                   |    |3223200*\/ 203144120309231113233 ||                                                                                         ___________________________________________________
                          |/          ___\     /                           _______________________ |             |atan|---------------------------------||     |                 |/          ___\     /                           _______________________ |             |atan|---------------------------------||                   |atan|---------------------------------|||                   |atan|---------------------------------||                             |/          ___\     /                           _______________________ |             |atan|---------------------------------||     |                 |/          ___\     /                           _______________________ |             |atan|---------------------------------||                   |atan|---------------------------------|||                   |atan|---------------------------------||                                                                                        /                           _______________________ 
                          ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|     |                 ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|            ___    |    \        53179606409624963        /||            ___    |    \        53179606409624963        /|                             ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|     |                 ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|            ___    |    \        53179606409624963        /||            ___    |    \        53179606409624963        /|                                                                                       /  53179606409624963   3*I*\/ 203144120309231113233  
                          ||- - - -------|*3 /   ----------------- + ----------------------------- |   412667*cos|---------------------------------------|     |                 ||- - - -------|*3 /   ----------------- + ----------------------------- |   412667*sin|---------------------------------------|   412667*\/ 3 *cos|---------------------------------------||   412667*\/ 3 *sin|---------------------------------------|                             ||- - + -------|*3 /   ----------------- + ----------------------------- |   412667*cos|---------------------------------------|     |                 ||- - + -------|*3 /   ----------------- + ----------------------------- |   412667*sin|---------------------------------------|   412667*\/ 3 *cos|---------------------------------------||   412667*\/ 3 *sin|---------------------------------------|                                                                                    3 /   ----------------- + ----------------------------- 
  412667                  \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /     |                 \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /                   \                   3                   /|                   \                   3                   /     412667                  \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /     |                 \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /                   \                   3                   /|                   \                   3                   /     412667                               170294052889                              \/     155027238848000              144291920           
- ------ - ----------------------------------------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- + ---------------------------------------------------------| - --------------------------------------------------------- + - ------ - ----------------------------------------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- - ---------------------------------------------------------| + --------------------------------------------------------- + - ------ - ------------------------------------------------------------------- - --------------------------------------------------------
  161160                                           8657515200                                                                 322320                           \                                          8657515200                                                                 322320                                                   322320                         /                             322320                              161160                                           8657515200                                                                 322320                           \                                          8657515200                                                                 322320                                                   322320                         /                             322320                              161160                   ___________________________________________________                              3                            
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /                           _______________________                                                            
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   /  53179606409624963   3*I*\/ 203144120309231113233                                                             
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     8657515200*3 /   ----------------- + -----------------------------                                                            
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                \/     155027238848000              144291920
((−412667161160−4126673sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320−170294052889re⁡(1(−12−3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200+412667cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+i(−170294052889im⁡(1(−12−3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200+412667sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+4126673cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320))+(−412667161160+4126673sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+412667cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320−170294052889re⁡(1(−12+3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200+i(−4126673cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+412667sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320−170294052889im⁡(1(−12+3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200)))+(−412667161160−53179606409624963155027238848000+3203144120309231113233i14429192033−170294052889865751520053179606409624963155027238848000+3203144120309231113233i1442919203)\left(\left(- \frac{412667}{161160} - \frac{412667 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + i \left(- \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320}\right)\right) + \left(- \frac{412667}{161160} + \frac{412667 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + i \left(- \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200}\right)\right)\right) + \left(- \frac{412667}{161160} - \frac{\sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}{3} - \frac{170294052889}{8657515200 \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right) 
=
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                                                                                 170294052889*re|------------------------------------------------------------------------|   170294052889*re|------------------------------------------------------------------------|                                                                        /    /          _______________________\\     |  170294052889*im|------------------------------------------------------------------------|             /    /          _______________________\\                   /    /          _______________________\\|     |  170294052889*im|------------------------------------------------------------------------|             /    /          _______________________\\                   /    /          _______________________\\|
                                                                                                |                     ___________________________________________________|                  |                     ___________________________________________________|        ___________________________________________________             |    |3223200*\/ 203144120309231113233 ||     |                 |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||                   |    |3223200*\/ 203144120309231113233 |||     |                 |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||                   |    |3223200*\/ 203144120309231113233 |||
                                                                                                |/          ___\     /                           _______________________ |                  |/          ___\     /                           _______________________ |       /                           _______________________              |atan|---------------------------------||     |                 |/          ___\     /                           _______________________ |             |atan|---------------------------------||                   |atan|---------------------------------|||     |                 |/          ___\     /                           _______________________ |             |atan|---------------------------------||                   |atan|---------------------------------|||
                                                                                                ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |                  ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |      /  53179606409624963   3*I*\/ 203144120309231113233               |    \        53179606409624963        /|     |                 ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|            ___    |    \        53179606409624963        /||     |                 ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|            ___    |    \        53179606409624963        /||
                                                                                                ||- - + -------|*3 /   ----------------- + ----------------------------- |                  ||- - - -------|*3 /   ----------------- + ----------------------------- |   3 /   ----------------- + -----------------------------    412667*cos|---------------------------------------|     |                 ||- - + -------|*3 /   ----------------- + ----------------------------- |   412667*sin|---------------------------------------|   412667*\/ 3 *cos|---------------------------------------||     |                 ||- - - -------|*3 /   ----------------- + ----------------------------- |   412667*sin|---------------------------------------|   412667*\/ 3 *cos|---------------------------------------||
  412667                               170294052889                                             \\  2      2   / \/     155027238848000              144291920           /                  \\  2      2   / \/     155027238848000              144291920           /   \/     155027238848000              144291920                        \                   3                   /     |                 \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /                   \                   3                   /|     |                 \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /                   \                   3                   /|
- ------ - ------------------------------------------------------------------- - ----------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------- - -------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- - ---------------------------------------------------------| + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- + ---------------------------------------------------------|
  53720                    ___________________________________________________                                           8657515200                                                                                  8657515200                                                                     3                                                      161160                           \                                          8657515200                                                                 322320                                                   322320                         /     \                                          8657515200                                                                 322320                                                   322320                         /
                          /                           _______________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                         /  53179606409624963   3*I*\/ 203144120309231113233                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
           8657515200*3 /   ----------------- + -----------------------------                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                      \/     155027238848000              144291920
−41266753720−170294052889re⁡(1(−12−3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200−170294052889re⁡(1(−12+3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200+412667cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)161160−53179606409624963155027238848000+3203144120309231113233i14429192033+i(−170294052889im⁡(1(−12−3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200+412667sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+4126673cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320)+i(−4126673cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+412667sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320−170294052889im⁡(1(−12+3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200)−170294052889865751520053179606409624963155027238848000+3203144120309231113233i1442919203- \frac{412667}{53720} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{161160} - \frac{\sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}{3} + i \left(- \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320}\right) + i \left(- \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200}\right) - \frac{170294052889}{8657515200 \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}} 
producto
/                          /                                   1                                    \                                                           /                 /                                   1                                    \                                                                                                                  \                                                            \ /                          /                                   1                                    \                                                           /                 /                                   1                                    \                                                                                                                  \                                                            \                                                                                                                                            
|           170294052889*re|------------------------------------------------------------------------|             /    /          _______________________\\     |  170294052889*im|------------------------------------------------------------------------|             /    /          _______________________\\                   /    /          _______________________\\|                   /    /          _______________________\\| |           170294052889*re|------------------------------------------------------------------------|             /    /          _______________________\\     |  170294052889*im|------------------------------------------------------------------------|             /    /          _______________________\\                   /    /          _______________________\\|                   /    /          _______________________\\|                                                                                                                                            
|                          |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||     |                 |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||                   |    |3223200*\/ 203144120309231113233 |||                   |    |3223200*\/ 203144120309231113233 ||| |                          |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||     |                 |                     ___________________________________________________|             |    |3223200*\/ 203144120309231113233 ||                   |    |3223200*\/ 203144120309231113233 |||                   |    |3223200*\/ 203144120309231113233 ||| /                                                                                      ___________________________________________________\
|                          |/          ___\     /                           _______________________ |             |atan|---------------------------------||     |                 |/          ___\     /                           _______________________ |             |atan|---------------------------------||                   |atan|---------------------------------|||                   |atan|---------------------------------||| |                          |/          ___\     /                           _______________________ |             |atan|---------------------------------||     |                 |/          ___\     /                           _______________________ |             |atan|---------------------------------||                   |atan|---------------------------------|||                   |atan|---------------------------------||| |                                                                                     /                           _______________________ |
|                          ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|     |                 ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|            ___    |    \        53179606409624963        /||            ___    |    \        53179606409624963        /|| |                          ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|     |                 ||  1   I*\/ 3 |    /  53179606409624963   3*I*\/ 203144120309231113233  |             |    \        53179606409624963        /|            ___    |    \        53179606409624963        /||            ___    |    \        53179606409624963        /|| |                                                                                    /  53179606409624963   3*I*\/ 203144120309231113233  |
|                          ||- - - -------|*3 /   ----------------- + ----------------------------- |   412667*cos|---------------------------------------|     |                 ||- - - -------|*3 /   ----------------- + ----------------------------- |   412667*sin|---------------------------------------|   412667*\/ 3 *cos|---------------------------------------||   412667*\/ 3 *sin|---------------------------------------|| |                          ||- - + -------|*3 /   ----------------- + ----------------------------- |   412667*cos|---------------------------------------|     |                 ||- - + -------|*3 /   ----------------- + ----------------------------- |   412667*sin|---------------------------------------|   412667*\/ 3 *cos|---------------------------------------||   412667*\/ 3 *sin|---------------------------------------|| |                                                                                 3 /   ----------------- + ----------------------------- |
|  412667                  \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /     |                 \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /                   \                   3                   /|                   \                   3                   /| |  412667                  \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /     |                 \\  2      2   / \/     155027238848000              144291920           /             \                   3                   /                   \                   3                   /|                   \                   3                   /| |  412667                               170294052889                              \/     155027238848000              144291920           |
|- ------ - ----------------------------------------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- + ---------------------------------------------------------| - ---------------------------------------------------------|*|- ------ - ----------------------------------------------------------------------------------------- + --------------------------------------------------- + I*|- ----------------------------------------------------------------------------------------- + --------------------------------------------------- - ---------------------------------------------------------| + ---------------------------------------------------------|*|- ------ - ------------------------------------------------------------------- - --------------------------------------------------------|
\  161160                                           8657515200                                                                 322320                           \                                          8657515200                                                                 322320                                                   322320                         /                             322320                         / \  161160                                           8657515200                                                                 322320                           \                                          8657515200                                                                 322320                                                   322320                         /                             322320                         / |  161160                   ___________________________________________________                              3                            |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |                         /  53179606409624963   3*I*\/ 203144120309231113233                                                             |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |           8657515200*3 /   ----------------- + -----------------------------                                                            |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          \                      \/     155027238848000              144291920                                                                      /
(−412667161160−4126673sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320−170294052889re⁡(1(−12−3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200+412667cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+i(−170294052889im⁡(1(−12−3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200+412667sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+4126673cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320))(−412667161160+4126673sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+412667cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320−170294052889re⁡(1(−12+3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200+i(−4126673cos⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320+412667sin⁡(atan⁡(322320020314412030923111323353179606409624963)3)322320−170294052889im⁡(1(−12+3i2)53179606409624963155027238848000+3203144120309231113233i1442919203)8657515200))(−412667161160−53179606409624963155027238848000+3203144120309231113233i14429192033−170294052889865751520053179606409624963155027238848000+3203144120309231113233i1442919203)\left(- \frac{412667}{161160} - \frac{412667 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + i \left(- \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320}\right)\right) \left(- \frac{412667}{161160} + \frac{412667 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200} + i \left(- \frac{412667 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} + \frac{412667 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}}{322320} - \frac{170294052889 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right)}}{8657515200}\right)\right) \left(- \frac{412667}{161160} - \frac{\sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}{3} - \frac{170294052889}{8657515200 \sqrt[3]{\frac{53179606409624963}{155027238848000} + \frac{3 \sqrt{203144120309231113233} i}{144291920}}}\right) 
=
                                                                                                                                                                   /     /      /          _______________________\\      /    /          _______________________\\\
                                                                                                                                                                   |     |      |3223200*\/ 203144120309231113233 ||      |    |3223200*\/ 203144120309231113233 |||
             /                  _________________________________________________________ /            _________________________________________________________\\ |     |2*atan|---------------------------------||      |atan|---------------------------------|||
             |               3 /                                 _______________________  |         3 /                                 _______________________ || |     |      \        53179606409624963        /|      |    \        53179606409624963        /||
170294052889*\170294052889 + \/  53179606409624963 + 3223200*I*\/ 203144120309231113233  *\412667 + \/  53179606409624963 + 3223200*I*\/ 203144120309231113233  //*|- cos|-----------------------------------------| + cos|---------------------------------------||
                                                                                                                                                                   \     \                    3                    /      \                   3                   //
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                               _________________________________________________________                                                                                            
                                                                                                            3 /                                 _______________________                                                                                             
                                                                                           2092867724448000*\/  53179606409624963 + 3223200*I*\/ 203144120309231113233
170294052889(170294052889+(412667+53179606409624963+3223200203144120309231113233i3)53179606409624963+3223200203144120309231113233i3)(−cos⁡(2atan⁡(322320020314412030923111323353179606409624963)3)+cos⁡(atan⁡(322320020314412030923111323353179606409624963)3))209286772444800053179606409624963+3223200203144120309231113233i3\frac{170294052889 \left(170294052889 + \left(412667 + \sqrt[3]{53179606409624963 + 3223200 \sqrt{203144120309231113233} i}\right) \sqrt[3]{53179606409624963 + 3223200 \sqrt{203144120309231113233} i}\right) \left(- \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)} + \cos{\left(\frac{\operatorname{atan}{\left(\frac{3223200 \sqrt{203144120309231113233}}{53179606409624963} \right)}}{3} \right)}\right)}{2092867724448000 \sqrt[3]{53179606409624963 + 3223200 \sqrt{203144120309231113233} i}} 
170294052889*(170294052889 + (53179606409624963 + 3223200*i*sqrt(203144120309231113233))^(1/3)*(412667 + (53179606409624963 + 3223200*i*sqrt(203144120309231113233))^(1/3)))*(-cos(2*atan(3223200*sqrt(203144120309231113233)/53179606409624963)/3) + cos(atan(3223200*sqrt(203144120309231113233)/53179606409624963)/3))/(2092867724448000*(53179606409624963 + 3223200*i*sqrt(203144120309231113233))^(1/3))
Respuesta numérica [src] 
x1 = -1.1153173930661
x2 = 0.971566283654639
x3 = -7.53806199557737
x3 = -7.53806199557737
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