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(-x)*(10+25/p)-60*x=-120+60/p la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   /     25\                 60
-x*|10 + --| - 60*x = -120 + --
   \     p /                 p
$$- x \left(10 + \frac{25}{p}\right) - 60 x = -120 + \frac{60}{p}$$
Simplificar
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$- x \left(10 + \frac{25}{p}\right) - 60 x = -120 + \frac{60}{p}$$
Коэффициент при x равен
$$-70 - \frac{25}{p}$$
entonces son posibles los casos para p :
$$p < - \frac{5}{14}$$
$$p = - \frac{5}{14}$$
Consideremos todos los casos con detalles:
Con
$$p < - \frac{5}{14}$$
la ecuación será
$$\frac{3120}{19} - \frac{980 x}{19} = 0$$
su solución
$$x = \frac{156}{49}$$
Con
$$p = - \frac{5}{14}$$
la ecuación será
$$288 = 0$$
su solución
no hay soluciones
Gráfica
Suma y producto de raíces [src] 
suma
                                                                                   2                                               
  /    168*(-1 + 2*re(p))*im(p)       24*(5 + 14*re(p))*im(p)   \            336*im (p)            12*(-1 + 2*re(p))*(5 + 14*re(p))
I*|- ---------------------------- + ----------------------------| + ---------------------------- + --------------------------------
  |                2         2                    2         2   |                 2         2                      2         2     
  \  (5 + 14*re(p))  + 196*im (p)   (5 + 14*re(p))  + 196*im (p)/   (5 + 14*re(p))  + 196*im (p)     (5 + 14*re(p))  + 196*im (p)
$$i \left(- \frac{168 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{24 \left(14 \operatorname{re}{\left(p\right)} + 5\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}\right) + \frac{12 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \left(14 \operatorname{re}{\left(p\right)} + 5\right)}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{336 \left(\operatorname{im}{\left(p\right)}\right)^{2}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}$$ 
=
                                                                                   2                                               
  /    168*(-1 + 2*re(p))*im(p)       24*(5 + 14*re(p))*im(p)   \            336*im (p)            12*(-1 + 2*re(p))*(5 + 14*re(p))
I*|- ---------------------------- + ----------------------------| + ---------------------------- + --------------------------------
  |                2         2                    2         2   |                 2         2                      2         2     
  \  (5 + 14*re(p))  + 196*im (p)   (5 + 14*re(p))  + 196*im (p)/   (5 + 14*re(p))  + 196*im (p)     (5 + 14*re(p))  + 196*im (p)
$$i \left(- \frac{168 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{24 \left(14 \operatorname{re}{\left(p\right)} + 5\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}\right) + \frac{12 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \left(14 \operatorname{re}{\left(p\right)} + 5\right)}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{336 \left(\operatorname{im}{\left(p\right)}\right)^{2}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}$$ 
producto
                                                                                   2                                               
  /    168*(-1 + 2*re(p))*im(p)       24*(5 + 14*re(p))*im(p)   \            336*im (p)            12*(-1 + 2*re(p))*(5 + 14*re(p))
I*|- ---------------------------- + ----------------------------| + ---------------------------- + --------------------------------
  |                2         2                    2         2   |                 2         2                      2         2     
  \  (5 + 14*re(p))  + 196*im (p)   (5 + 14*re(p))  + 196*im (p)/   (5 + 14*re(p))  + 196*im (p)     (5 + 14*re(p))  + 196*im (p)
$$i \left(- \frac{168 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{24 \left(14 \operatorname{re}{\left(p\right)} + 5\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}\right) + \frac{12 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \left(14 \operatorname{re}{\left(p\right)} + 5\right)}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{336 \left(\operatorname{im}{\left(p\right)}\right)^{2}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}$$ 
=
   /     2                                                \
12*\28*im (p) + (-1 + 2*re(p))*(5 + 14*re(p)) + 24*I*im(p)/
-----------------------------------------------------------
                              2         2                  
                (5 + 14*re(p))  + 196*im (p)
$$\frac{12 \left(\left(2 \operatorname{re}{\left(p\right)} - 1\right) \left(14 \operatorname{re}{\left(p\right)} + 5\right) + 28 \left(\operatorname{im}{\left(p\right)}\right)^{2} + 24 i \operatorname{im}{\left(p\right)}\right)}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}$$ 
12*(28*im(p)^2 + (-1 + 2*re(p))*(5 + 14*re(p)) + 24*i*im(p))/((5 + 14*re(p))^2 + 196*im(p)^2)
Respuesta rápida [src] 
                                                                                        2                                               
       /    168*(-1 + 2*re(p))*im(p)       24*(5 + 14*re(p))*im(p)   \            336*im (p)            12*(-1 + 2*re(p))*(5 + 14*re(p))
x1 = I*|- ---------------------------- + ----------------------------| + ---------------------------- + --------------------------------
       |                2         2                    2         2   |                 2         2                      2         2     
       \  (5 + 14*re(p))  + 196*im (p)   (5 + 14*re(p))  + 196*im (p)/   (5 + 14*re(p))  + 196*im (p)     (5 + 14*re(p))  + 196*im (p)
$$x_{1} = i \left(- \frac{168 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{24 \left(14 \operatorname{re}{\left(p\right)} + 5\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}\right) + \frac{12 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \left(14 \operatorname{re}{\left(p\right)} + 5\right)}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{336 \left(\operatorname{im}{\left(p\right)}\right)^{2}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}$$ 
x1 = i*(-168*(2*re(p) - 1)*im(p)/((14*re(p) + 5)^2 + 196*im(p)^2) + 24*(14*re(p) + 5)*im(p)/((14*re(p) + 5)^2 + 196*im(p)^2)) + 12*(2*re(p) - 1)*(14*re(p) + 5)/((14*re(p) + 5)^2 + 196*im(p)^2) + 336*im(p)^2/((14*re(p) + 5)^2 + 196*im(p)^2)
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