2x^2/(1-x)(1-x)=46

Solution for 2x^2/(1-x)(1-x)=46 equation:

2x^2/(1-x)(1-x)=46

We move all terms to the left:

2x^2/(1-x)(1-x)-(46)=0


Domain of the equation: (1-x)(1-x)!=0

We move all terms containing x to the left, all other terms to the right

-x)(1-x!=-1

x∈R


We add all the numbers together, and all the variables

2x^2/(-1x+1)(-1x+1)-46=0

We multiply parentheses ..

2x^2/(+x^2-1x-1x+1)-46=0

We multiply all the terms by the denominator


2x^2-46*(+x^2-1x-1x+1)=0

We multiply parentheses

2x^2-46x^2+46x+46x-46=0

We add all the numbers together, and all the variables

-44x^2+92x-46=0

a = -44; b = 92; c = -46;
Δ = b2-4ac
Δ = 922-4·(-44)·(-46)
Δ = 368
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-4\sqrt{23}}{2*-44}=\frac{-92-4\sqrt{23}}{-88}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+4\sqrt{23}}{2*-44}=\frac{-92+4\sqrt{23}}{-88}
$