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ax+b=cx+d la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
a*x + b = c*x + d
ax+b=cx+da x + b = c x + d
Simplificar
Solución detallada
Tenemos una ecuación lineal:
a*x+b = c*x+d

Dividamos ambos miembros de la ecuación en (b + a*x)/x
x = d + c*x / ((b + a*x)/x)

Obtenemos la respuesta: x = (d - b)/(a - c)
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
ax+b=cx+da x + b = c x + d
Коэффициент при x равен
a−ca - c
entonces son posibles los casos para a :
a<ca < c
a=ca = c
Consideremos todos los casos con detalles:
Con
a<ca < c
la ecuación será
b−cx−d+x(c−1)=0b - c x - d + x \left(c - 1\right) = 0
su solución
x=b−dx = b - d
Con
a=ca = c
la ecuación será
b−d=0b - d = 0
su solución
Gráfica
Respuesta rápida [src] 
       /  (-im(a) + im(c))*(-re(b) + re(d))       (-im(b) + im(d))*(-re(c) + re(a))  \     (-re(b) + re(d))*(-re(c) + re(a))       (-im(a) + im(c))*(-im(b) + im(d))  
x1 = I*|------------------------------------- + -------------------------------------| + ------------------------------------- - -------------------------------------
       |                2                   2                   2                   2|                   2                   2                   2                   2
       \(-im(c) + im(a))  + (-re(c) + re(a))    (-im(c) + im(a))  + (-re(c) + re(a)) /   (-im(c) + im(a))  + (-re(c) + re(a))    (-im(c) + im(a))  + (-re(c) + re(a))
x1=i((re⁡(a)−re⁡(c))(−im⁡(b)+im⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2+(−re⁡(b)+re⁡(d))(−im⁡(a)+im⁡(c))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2)+(re⁡(a)−re⁡(c))(−re⁡(b)+re⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2−(−im⁡(a)+im⁡(c))(−im⁡(b)+im⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2x_{1} = i \left(\frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right) \left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} - \frac{\left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} 
x1 = i*((re(a) - re(c))*(-im(b) + im(d))/((re(a) - re(c))^2 + (im(a) - im(c))^2) + (-re(b) + re(d))*(-im(a) + im(c))/((re(a) - re(c))^2 + (im(a) - im(c))^2)) + (re(a) - re(c))*(-re(b) + re(d))/((re(a) - re(c))^2 + (im(a) - im(c))^2) - (-im(a) + im(c))*(-im(b) + im(d))/((re(a) - re(c))^2 + (im(a) - im(c))^2)
Suma y producto de raíces [src] 
suma
  /  (-im(a) + im(c))*(-re(b) + re(d))       (-im(b) + im(d))*(-re(c) + re(a))  \     (-re(b) + re(d))*(-re(c) + re(a))       (-im(a) + im(c))*(-im(b) + im(d))  
I*|------------------------------------- + -------------------------------------| + ------------------------------------- - -------------------------------------
  |                2                   2                   2                   2|                   2                   2                   2                   2
  \(-im(c) + im(a))  + (-re(c) + re(a))    (-im(c) + im(a))  + (-re(c) + re(a)) /   (-im(c) + im(a))  + (-re(c) + re(a))    (-im(c) + im(a))  + (-re(c) + re(a))
i((re⁡(a)−re⁡(c))(−im⁡(b)+im⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2+(−re⁡(b)+re⁡(d))(−im⁡(a)+im⁡(c))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2)+(re⁡(a)−re⁡(c))(−re⁡(b)+re⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2−(−im⁡(a)+im⁡(c))(−im⁡(b)+im⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2i \left(\frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right) \left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} - \frac{\left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} 
=
  /  (-im(a) + im(c))*(-re(b) + re(d))       (-im(b) + im(d))*(-re(c) + re(a))  \     (-re(b) + re(d))*(-re(c) + re(a))       (-im(a) + im(c))*(-im(b) + im(d))  
I*|------------------------------------- + -------------------------------------| + ------------------------------------- - -------------------------------------
  |                2                   2                   2                   2|                   2                   2                   2                   2
  \(-im(c) + im(a))  + (-re(c) + re(a))    (-im(c) + im(a))  + (-re(c) + re(a)) /   (-im(c) + im(a))  + (-re(c) + re(a))    (-im(c) + im(a))  + (-re(c) + re(a))
i((re⁡(a)−re⁡(c))(−im⁡(b)+im⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2+(−re⁡(b)+re⁡(d))(−im⁡(a)+im⁡(c))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2)+(re⁡(a)−re⁡(c))(−re⁡(b)+re⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2−(−im⁡(a)+im⁡(c))(−im⁡(b)+im⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2i \left(\frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right) \left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} - \frac{\left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} 
producto
  /  (-im(a) + im(c))*(-re(b) + re(d))       (-im(b) + im(d))*(-re(c) + re(a))  \     (-re(b) + re(d))*(-re(c) + re(a))       (-im(a) + im(c))*(-im(b) + im(d))  
I*|------------------------------------- + -------------------------------------| + ------------------------------------- - -------------------------------------
  |                2                   2                   2                   2|                   2                   2                   2                   2
  \(-im(c) + im(a))  + (-re(c) + re(a))    (-im(c) + im(a))  + (-re(c) + re(a)) /   (-im(c) + im(a))  + (-re(c) + re(a))    (-im(c) + im(a))  + (-re(c) + re(a))
i((re⁡(a)−re⁡(c))(−im⁡(b)+im⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2+(−re⁡(b)+re⁡(d))(−im⁡(a)+im⁡(c))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2)+(re⁡(a)−re⁡(c))(−re⁡(b)+re⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2−(−im⁡(a)+im⁡(c))(−im⁡(b)+im⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2i \left(\frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right) \left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} - \frac{\left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} 
=
I*((-im(c) + im(a))*(-re(d) + re(b)) - (-im(d) + im(b))*(-re(c) + re(a))) - (-im(c) + im(a))*(-im(d) + im(b)) - (-re(c) + re(a))*(-re(d) + re(b))
-------------------------------------------------------------------------------------------------------------------------------------------------
                                                                      2                   2                                                      
                                                      (-im(c) + im(a))  + (-re(c) + re(a))
i(−(re⁡(a)−re⁡(c))(im⁡(b)−im⁡(d))+(re⁡(b)−re⁡(d))(im⁡(a)−im⁡(c)))−(re⁡(a)−re⁡(c))(re⁡(b)−re⁡(d))−(im⁡(a)−im⁡(c))(im⁡(b)−im⁡(d))(re⁡(a)−re⁡(c))2+(im⁡(a)−im⁡(c))2\frac{i \left(- \left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(b\right)} - \operatorname{im}{\left(d\right)}\right) + \left(\operatorname{re}{\left(b\right)} - \operatorname{re}{\left(d\right)}\right) \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)\right) - \left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(\operatorname{re}{\left(b\right)} - \operatorname{re}{\left(d\right)}\right) - \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right) \left(\operatorname{im}{\left(b\right)} - \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} 
(i*((-im(c) + im(a))*(-re(d) + re(b)) - (-im(d) + im(b))*(-re(c) + re(a))) - (-im(c) + im(a))*(-im(d) + im(b)) - (-re(c) + re(a))*(-re(d) + re(b)))/((-im(c) + im(a))^2 + (-re(c) + re(a))^2)
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