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cospi(4*x-6)/3=12 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
cos(p)*I*(4*x - 6)     
------------------ = 12
        3
icos⁡(p)(4x−6)3=12\frac{i \cos{\left(p \right)} \left(4 x - 6\right)}{3} = 12
Simplificar
Solución detallada
Tenemos la ecuación
icos⁡(p)(4x−6)3=12\frac{i \cos{\left(p \right)} \left(4 x - 6\right)}{3} = 12
cambiamos
2i(2x−3)cos⁡(p)3−13=0\frac{2 i \left(2 x - 3\right) \cos{\left(p \right)}}{3} - 13 = 0
icos⁡(p)(4x−6)3−13=0\frac{i \cos{\left(p \right)} \left(4 x - 6\right)}{3} - 13 = 0
Sustituimos
w=cos⁡(p)w = \cos{\left(p \right)}
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-13 + i*w4*x/3+6/3 = 0

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-13 + i*w*(-6 + 4*x)/3 = 0

Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
iw(4x−6)3=13\frac{i w \left(4 x - 6\right)}{3} = 13
Dividamos ambos miembros de la ecuación en i*(-6 + 4*x)/3
w = 13 / (i*(-6 + 4*x)/3)

Obtenemos la respuesta: w = -39*i/(-6 + 4*x)
hacemos cambio inverso
cos⁡(p)=w\cos{\left(p \right)} = w
sustituimos w:
Gráfica
Suma y producto de raíces [src] 
suma
3                 9*sin(re(p))*sinh(im(p))                             9*I*cos(re(p))*cosh(im(p))            
- + --------------------------------------------------- - ---------------------------------------------------
2      2            2             2            2             2            2             2            2       
    cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))   cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
32+9sin⁡(re⁡(p))sinh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))−9icos⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))\frac{3}{2} + \frac{9 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{9 i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} 
=
3                 9*sin(re(p))*sinh(im(p))                             9*I*cos(re(p))*cosh(im(p))            
- + --------------------------------------------------- - ---------------------------------------------------
2      2            2             2            2             2            2             2            2       
    cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))   cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
32+9sin⁡(re⁡(p))sinh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))−9icos⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))\frac{3}{2} + \frac{9 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{9 i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} 
producto
3                 9*sin(re(p))*sinh(im(p))                             9*I*cos(re(p))*cosh(im(p))            
- + --------------------------------------------------- - ---------------------------------------------------
2      2            2             2            2             2            2             2            2       
    cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))   cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
32+9sin⁡(re⁡(p))sinh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))−9icos⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))\frac{3}{2} + \frac{9 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{9 i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} 
=
3*(I*(6 + sin(re(p))*sinh(im(p))) - cos(re(p))*cosh(im(p)))
-----------------------------------------------------------
   2*(-cos(re(p))*cosh(im(p)) + I*sin(re(p))*sinh(im(p)))
3(i(sin⁡(re⁡(p))sinh⁡(im⁡(p))+6)−cos⁡(re⁡(p))cosh⁡(im⁡(p)))2(isin⁡(re⁡(p))sinh⁡(im⁡(p))−cos⁡(re⁡(p))cosh⁡(im⁡(p)))\frac{3 \left(i \left(\sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + 6\right) - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}\right)}{2 \left(i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}\right)} 
3*(i*(6 + sin(re(p))*sinh(im(p))) - cos(re(p))*cosh(im(p)))/(2*(-cos(re(p))*cosh(im(p)) + i*sin(re(p))*sinh(im(p))))
Respuesta rápida [src] 
     3                 9*sin(re(p))*sinh(im(p))                             9*I*cos(re(p))*cosh(im(p))            
x1 = - + --------------------------------------------------- - ---------------------------------------------------
     2      2            2             2            2             2            2             2            2       
         cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))   cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
x1=32+9sin⁡(re⁡(p))sinh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))−9icos⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))x_{1} = \frac{3}{2} + \frac{9 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{9 i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} 
x1 = 3/2 + 9*sin(re(p))*sinh(im(p))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2) - 9*i*cos(re(p))*cosh(im(p))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2)
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