2x^2/(1-x)(2-x)=115

Solution for 2x^2/(1-x)(2-x)=115 equation:

2x^2/(1-x)(2-x)=115

We move all terms to the left:

2x^2/(1-x)(2-x)-(115)=0


Domain of the equation: (1-x)(2-x)!=0

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

-x)(2-x!=-1

x∈R


We add all the numbers together, and all the variables

2x^2/(-1x+1)(-1x+2)-115=0

We multiply parentheses ..

2x^2/(+x^2-2x-1x+2)-115=0

We multiply all the terms by the denominator


2x^2-115*(+x^2-2x-1x+2)=0

We multiply parentheses

2x^2-115x^2+230x+115x-230=0

We add all the numbers together, and all the variables

-113x^2+345x-230=0

a = -113; b = 345; c = -230;
Δ = b2-4ac
Δ = 3452-4·(-113)·(-230)
Δ = 15065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(345)-\sqrt{15065}}{2*-113}=\frac{-345-\sqrt{15065}}{-226}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(345)+\sqrt{15065}}{2*-113}=\frac{-345+\sqrt{15065}}{-226}
$