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x^3+7*x^2-20*x-72=0 la ecuación

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v

Solución numérica:

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Solución

Ha introducido [src] 
 3      2                
x  + 7*x  - 20*x - 72 = 0
(−20x+(x3+7x2))−72=0\left(- 20 x + \left(x^{3} + 7 x^{2}\right)\right) - 72 = 0
Simplificar
Teorema de Cardano-Vieta
es ecuación cúbica reducida
px2+qx+v+x3=0p x^{2} + q x + v + x^{3} = 0
donde
p=bap = \frac{b}{a}
p=7p = 7
q=caq = \frac{c}{a}
q=−20q = -20
v=dav = \frac{d}{a}
v=−72v = -72
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=−7x_{1} + x_{2} + x_{3} = -7
x1x2+x1x3+x2x3=−20x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -20
x1x2x3=−72x_{1} x_{2} x_{3} = -72
Respuesta rápida [src] 
                 /                  1                   \     /        /                  1                   \                                                                  \                                                                  
           109*re|--------------------------------------|     |  109*im|--------------------------------------|                                                                  |                                                                  
                 |   ___________________ /          ___\|     |        |   ___________________ /          ___\|              /    /     ______\\              /    /     ______\\|              /    /     ______\\              /    /     ______\\
                 |3 /            ______  |  1   I*\/ 3 ||     |        |3 /            ______  |  1   I*\/ 3 ||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /|
                 |\/  1 + 18*I*\/ 3997  *|- - - -------||     |        |\/  1 + 18*I*\/ 3997  *|- - - -------||   \/ 109 *sin|-----------------|   \/ 327 *cos|-----------------||   \/ 327 *sin|-----------------|   \/ 109 *cos|-----------------|
       7         \                       \  2      2   //     |        \                       \  2      2   //              \        3        /              \        3        /|              \        3        /              \        3        /
x1 = - - - ---------------------------------------------- + I*|- ---------------------------------------------- + ------------------------------ + ------------------------------| - ------------------------------ + ------------------------------
       3                         3                            \                        3                                        6                                6               /                 6                                6
x1=−73−327sin⁡(atan⁡(183997)3)6−109re⁡(1(−12−3i2)1+183997i3)3+109cos⁡(atan⁡(183997)3)6+i(−109im⁡(1(−12−3i2)1+183997i3)3+109sin⁡(atan⁡(183997)3)6+327cos⁡(atan⁡(183997)3)6)x_{1} = - \frac{7}{3} - \frac{\sqrt{327} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} - \frac{109 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3} + \frac{\sqrt{109} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + i \left(- \frac{109 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3} + \frac{\sqrt{109} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + \frac{\sqrt{327} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6}\right) 
                 /                  1                   \     /        /                  1                   \                                                                  \                                                                  
           109*re|--------------------------------------|     |  109*im|--------------------------------------|                                                                  |                                                                  
                 |   ___________________ /          ___\|     |        |   ___________________ /          ___\|              /    /     ______\\              /    /     ______\\|              /    /     ______\\              /    /     ______\\
                 |3 /            ______  |  1   I*\/ 3 ||     |        |3 /            ______  |  1   I*\/ 3 ||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /|
                 |\/  1 + 18*I*\/ 3997  *|- - + -------||     |        |\/  1 + 18*I*\/ 3997  *|- - + -------||   \/ 327 *cos|-----------------|   \/ 109 *sin|-----------------||   \/ 109 *cos|-----------------|   \/ 327 *sin|-----------------|
       7         \                       \  2      2   //     |        \                       \  2      2   //              \        3        /              \        3        /|              \        3        /              \        3        /
x2 = - - - ---------------------------------------------- + I*|- ---------------------------------------------- - ------------------------------ + ------------------------------| + ------------------------------ + ------------------------------
       3                         3                            \                        3                                        6                                6               /                 6                                6
x2=−73+327sin⁡(atan⁡(183997)3)6+109cos⁡(atan⁡(183997)3)6−109re⁡(1(−12+3i2)1+183997i3)3+i(−327cos⁡(atan⁡(183997)3)6+109sin⁡(atan⁡(183997)3)6−109im⁡(1(−12+3i2)1+183997i3)3)x_{2} = - \frac{7}{3} + \frac{\sqrt{327} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + \frac{\sqrt{109} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} - \frac{109 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3} + i \left(- \frac{\sqrt{327} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + \frac{\sqrt{109} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} - \frac{109 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3}\right) 
                                         ___________________
                                      3 /            ______ 
       7             109              \/  1 + 18*I*\/ 3997  
x3 = - - - ------------------------ - ----------------------
       3        ___________________             3           
             3 /            ______                          
           3*\/  1 + 18*I*\/ 3997
x3=−73−1+183997i33−10931+183997i3x_{3} = - \frac{7}{3} - \frac{\sqrt[3]{1 + 18 \sqrt{3997} i}}{3} - \frac{109}{3 \sqrt[3]{1 + 18 \sqrt{3997} i}} 
x3 = -7/3 - (1 + 18*sqrt(3997)*i)^(1/3)/3 - 109/(3*(1 + 18*sqrt(3997)*i)^(1/3))
Suma y producto de raíces [src] 
suma
            /                  1                   \     /        /                  1                   \                                                                  \                                                                                 /                  1                   \     /        /                  1                   \                                                                  \                                                                                                                            
      109*re|--------------------------------------|     |  109*im|--------------------------------------|                                                                  |                                                                           109*re|--------------------------------------|     |  109*im|--------------------------------------|                                                                  |                                                                                                                            
            |   ___________________ /          ___\|     |        |   ___________________ /          ___\|              /    /     ______\\              /    /     ______\\|              /    /     ______\\              /    /     ______\\               |   ___________________ /          ___\|     |        |   ___________________ /          ___\|              /    /     ______\\              /    /     ______\\|              /    /     ______\\              /    /     ______\\                                                          
            |3 /            ______  |  1   I*\/ 3 ||     |        |3 /            ______  |  1   I*\/ 3 ||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /|               |3 /            ______  |  1   I*\/ 3 ||     |        |3 /            ______  |  1   I*\/ 3 ||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /|                                       ___________________
            |\/  1 + 18*I*\/ 3997  *|- - - -------||     |        |\/  1 + 18*I*\/ 3997  *|- - - -------||   \/ 109 *sin|-----------------|   \/ 327 *cos|-----------------||   \/ 327 *sin|-----------------|   \/ 109 *cos|-----------------|               |\/  1 + 18*I*\/ 3997  *|- - + -------||     |        |\/  1 + 18*I*\/ 3997  *|- - + -------||   \/ 327 *cos|-----------------|   \/ 109 *sin|-----------------||   \/ 109 *cos|-----------------|   \/ 327 *sin|-----------------|                                    3 /            ______ 
  7         \                       \  2      2   //     |        \                       \  2      2   //              \        3        /              \        3        /|              \        3        /              \        3        /     7         \                       \  2      2   //     |        \                       \  2      2   //              \        3        /              \        3        /|              \        3        /              \        3        /     7             109              \/  1 + 18*I*\/ 3997  
- - - ---------------------------------------------- + I*|- ---------------------------------------------- + ------------------------------ + ------------------------------| - ------------------------------ + ------------------------------ + - - - ---------------------------------------------- + I*|- ---------------------------------------------- - ------------------------------ + ------------------------------| + ------------------------------ + ------------------------------ + - - - ------------------------ - ----------------------
  3                         3                            \                        3                                        6                                6               /                 6                                6                    3                         3                            \                        3                                        6                                6               /                 6                                6                    3        ___________________             3           
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            3 /            ______                          
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          3*\/  1 + 18*I*\/ 3997
(−73−1+183997i33−10931+183997i3)+((−73−327sin⁡(atan⁡(183997)3)6−109re⁡(1(−12−3i2)1+183997i3)3+109cos⁡(atan⁡(183997)3)6+i(−109im⁡(1(−12−3i2)1+183997i3)3+109sin⁡(atan⁡(183997)3)6+327cos⁡(atan⁡(183997)3)6))+(−73+327sin⁡(atan⁡(183997)3)6+109cos⁡(atan⁡(183997)3)6−109re⁡(1(−12+3i2)1+183997i3)3+i(−327cos⁡(atan⁡(183997)3)6+109sin⁡(atan⁡(183997)3)6−109im⁡(1(−12+3i2)1+183997i3)3)))\left(- \frac{7}{3} - \frac{\sqrt[3]{1 + 18 \sqrt{3997} i}}{3} - \frac{109}{3 \sqrt[3]{1 + 18 \sqrt{3997} i}}\right) + \left(\left(- \frac{7}{3} - \frac{\sqrt{327} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} - \frac{109 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3} + \frac{\sqrt{109} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + i \left(- \frac{109 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3} + \frac{\sqrt{109} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + \frac{\sqrt{327} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6}\right)\right) + \left(- \frac{7}{3} + \frac{\sqrt{327} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + \frac{\sqrt{109} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} - \frac{109 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3} + i \left(- \frac{\sqrt{327} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + \frac{\sqrt{109} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} - \frac{109 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3}\right)\right)\right) 
=
                                      /                  1                   \         /                  1                   \                              /        /                  1                   \                                                                  \     /        /                  1                   \                                                                  \                                 
                                109*re|--------------------------------------|   109*re|--------------------------------------|                              |  109*im|--------------------------------------|                                                                  |     |  109*im|--------------------------------------|                                                                  |                                 
                                      |   ___________________ /          ___\|         |   ___________________ /          ___\|                              |        |   ___________________ /          ___\|              /    /     ______\\              /    /     ______\\|     |        |   ___________________ /          ___\|              /    /     ______\\              /    /     ______\\|              /    /     ______\\
                                      |3 /            ______  |  1   I*\/ 3 ||         |3 /            ______  |  1   I*\/ 3 ||      ___________________     |        |3 /            ______  |  1   I*\/ 3 ||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /||     |        |3 /            ______  |  1   I*\/ 3 ||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /||     _____    |atan\18*\/ 3997 /|
                                      |\/  1 + 18*I*\/ 3997  *|- - + -------||         |\/  1 + 18*I*\/ 3997  *|- - - -------||   3 /            ______      |        |\/  1 + 18*I*\/ 3997  *|- - + -------||   \/ 327 *cos|-----------------|   \/ 109 *sin|-----------------||     |        |\/  1 + 18*I*\/ 3997  *|- - - -------||   \/ 109 *sin|-----------------|   \/ 327 *cos|-----------------||   \/ 109 *cos|-----------------|
               109                    \                       \  2      2   //         \                       \  2      2   //   \/  1 + 18*I*\/ 3997       |        \                       \  2      2   //              \        3        /              \        3        /|     |        \                       \  2      2   //              \        3        /              \        3        /|              \        3        /
-7 - ------------------------ - ---------------------------------------------- - ---------------------------------------------- - ---------------------- + I*|- ---------------------------------------------- - ------------------------------ + ------------------------------| + I*|- ---------------------------------------------- + ------------------------------ + ------------------------------| + ------------------------------
          ___________________                         3                                                3                                    3                \                        3                                        6                                6               /     \                        3                                        6                                6               /                 3               
       3 /            ______                                                                                                                                                                                                                                                                                                                                                                                                               
     3*\/  1 + 18*I*\/ 3997
−7−109re⁡(1(−12−3i2)1+183997i3)3−109re⁡(1(−12+3i2)1+183997i3)3+109cos⁡(atan⁡(183997)3)3−1+183997i33+i(−109im⁡(1(−12−3i2)1+183997i3)3+109sin⁡(atan⁡(183997)3)6+327cos⁡(atan⁡(183997)3)6)+i(−327cos⁡(atan⁡(183997)3)6+109sin⁡(atan⁡(183997)3)6−109im⁡(1(−12+3i2)1+183997i3)3)−10931+183997i3-7 - \frac{109 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3} - \frac{109 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3} + \frac{\sqrt{109} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{3} - \frac{\sqrt[3]{1 + 18 \sqrt{3997} i}}{3} + i \left(- \frac{109 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3} + \frac{\sqrt{109} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + \frac{\sqrt{327} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6}\right) + i \left(- \frac{\sqrt{327} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + \frac{\sqrt{109} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} - \frac{109 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3}\right) - \frac{109}{3 \sqrt[3]{1 + 18 \sqrt{3997} i}} 
producto
/            /                  1                   \     /        /                  1                   \                                                                  \                                                                  \ /            /                  1                   \     /        /                  1                   \                                                                  \                                                                  \                                                          
|      109*re|--------------------------------------|     |  109*im|--------------------------------------|                                                                  |                                                                  | |      109*re|--------------------------------------|     |  109*im|--------------------------------------|                                                                  |                                                                  |                                                          
|            |   ___________________ /          ___\|     |        |   ___________________ /          ___\|              /    /     ______\\              /    /     ______\\|              /    /     ______\\              /    /     ______\\| |            |   ___________________ /          ___\|     |        |   ___________________ /          ___\|              /    /     ______\\              /    /     ______\\|              /    /     ______\\              /    /     ______\\|                                                          
|            |3 /            ______  |  1   I*\/ 3 ||     |        |3 /            ______  |  1   I*\/ 3 ||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /|| |            |3 /            ______  |  1   I*\/ 3 ||     |        |3 /            ______  |  1   I*\/ 3 ||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /||     _____    |atan\18*\/ 3997 /|     _____    |atan\18*\/ 3997 /|| /                                    ___________________\
|            |\/  1 + 18*I*\/ 3997  *|- - - -------||     |        |\/  1 + 18*I*\/ 3997  *|- - - -------||   \/ 109 *sin|-----------------|   \/ 327 *cos|-----------------||   \/ 327 *sin|-----------------|   \/ 109 *cos|-----------------|| |            |\/  1 + 18*I*\/ 3997  *|- - + -------||     |        |\/  1 + 18*I*\/ 3997  *|- - + -------||   \/ 327 *cos|-----------------|   \/ 109 *sin|-----------------||   \/ 109 *cos|-----------------|   \/ 327 *sin|-----------------|| |                                 3 /            ______ |
|  7         \                       \  2      2   //     |        \                       \  2      2   //              \        3        /              \        3        /|              \        3        /              \        3        /| |  7         \                       \  2      2   //     |        \                       \  2      2   //              \        3        /              \        3        /|              \        3        /              \        3        /| |  7             109              \/  1 + 18*I*\/ 3997  |
|- - - ---------------------------------------------- + I*|- ---------------------------------------------- + ------------------------------ + ------------------------------| - ------------------------------ + ------------------------------|*|- - - ---------------------------------------------- + I*|- ---------------------------------------------- - ------------------------------ + ------------------------------| + ------------------------------ + ------------------------------|*|- - - ------------------------ - ----------------------|
\  3                         3                            \                        3                                        6                                6               /                 6                                6               / \  3                         3                            \                        3                                        6                                6               /                 6                                6               / |  3        ___________________             3           |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |        3 /            ______                          |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    \      3*\/  1 + 18*I*\/ 3997                           /
(−73−327sin⁡(atan⁡(183997)3)6−109re⁡(1(−12−3i2)1+183997i3)3+109cos⁡(atan⁡(183997)3)6+i(−109im⁡(1(−12−3i2)1+183997i3)3+109sin⁡(atan⁡(183997)3)6+327cos⁡(atan⁡(183997)3)6))(−73+327sin⁡(atan⁡(183997)3)6+109cos⁡(atan⁡(183997)3)6−109re⁡(1(−12+3i2)1+183997i3)3+i(−327cos⁡(atan⁡(183997)3)6+109sin⁡(atan⁡(183997)3)6−109im⁡(1(−12+3i2)1+183997i3)3))(−73−1+183997i33−10931+183997i3)\left(- \frac{7}{3} - \frac{\sqrt{327} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} - \frac{109 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3} + \frac{\sqrt{109} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + i \left(- \frac{109 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3} + \frac{\sqrt{109} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + \frac{\sqrt{327} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6}\right)\right) \left(- \frac{7}{3} + \frac{\sqrt{327} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + \frac{\sqrt{109} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} - \frac{109 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3} + i \left(- \frac{\sqrt{327} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} + \frac{\sqrt{109} \sin{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}}{6} - \frac{109 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{1 + 18 \sqrt{3997} i}}\right)}}{3}\right)\right) \left(- \frac{7}{3} - \frac{\sqrt[3]{1 + 18 \sqrt{3997} i}}{3} - \frac{109}{3 \sqrt[3]{1 + 18 \sqrt{3997} i}}\right) 
=
/         ___________________ /       ___________________\\ /            /      /     ______\\                 /    /     ______\\\
|      3 /            ______  |    3 /            ______ || |            |2*atan\18*\/ 3997 /|        _____    |atan\18*\/ 3997 /||
\109 + \/  1 + 18*I*\/ 3997  *\7 + \/  1 + 18*I*\/ 3997  //*|60 - 218*cos|-------------------| + 14*\/ 109 *cos|-----------------||
                                                            \            \         3         /                 \        3        //
-----------------------------------------------------------------------------------------------------------------------------------
                                                           ___________________                                                     
                                                        3 /            ______                                                      
                                                     27*\/  1 + 18*I*\/ 3997
(109+1+183997i3(7+1+183997i3))(−218cos⁡(2atan⁡(183997)3)+60+14109cos⁡(atan⁡(183997)3))271+183997i3\frac{\left(109 + \sqrt[3]{1 + 18 \sqrt{3997} i} \left(7 + \sqrt[3]{1 + 18 \sqrt{3997} i}\right)\right) \left(- 218 \cos{\left(\frac{2 \operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)} + 60 + 14 \sqrt{109} \cos{\left(\frac{\operatorname{atan}{\left(18 \sqrt{3997} \right)}}{3} \right)}\right)}{27 \sqrt[3]{1 + 18 \sqrt{3997} i}} 
(109 + (1 + 18*i*sqrt(3997))^(1/3)*(7 + (1 + 18*i*sqrt(3997))^(1/3)))*(60 - 218*cos(2*atan(18*sqrt(3997))/3) + 14*sqrt(109)*cos(atan(18*sqrt(3997))/3))/(27*(1 + 18*i*sqrt(3997))^(1/3))
Respuesta numérica [src] 
x1 = 3.69336081331646
x2 = -8.36206621620005
x3 = -2.33129459711642
x3 = -2.33129459711642
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