115=4x^2/(1-x)(2-x)

Solution for 115=4x^2/(1-x)(2-x) equation:

115=4x^2/(1-x)(2-x)

We move all terms to the left:

115-(4x^2/(1-x)(2-x))=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

-(4x^2/(-1x+1)(-1x+2))+115=0

We multiply parentheses ..

-(4x^2/(+x^2-2x-1x+2))+115=0

We multiply all the terms by the denominator


-(4x^2+115*(+x^2-2x-1x+2))=0


We calculate terms in parentheses: -(4x^2+115*(+x^2-2x-1x+2)), so:

4x^2+115*(+x^2-2x-1x+2)

We multiply parentheses

4x^2+115x^2-230x-115x+230

We add all the numbers together, and all the variables

119x^2-345x+230

Back to the equation:

-(119x^2-345x+230)


We get rid of parentheses

-119x^2+345x-230=0

a = -119; b = 345; c = -230;
Δ = b2-4ac
Δ = 3452-4·(-119)·(-230)
Δ = 9545
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{9545}}{2*-119}=\frac{-345-\sqrt{9545}}{-238}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(345)+\sqrt{9545}}{2*-119}=\frac{-345+\sqrt{9545}}{-238}
$