115=(2x^2)/(1.00-x)*(2.00-x)

Solution for 115=(2x^2)/(1.00-x)*(2.00-x) equation:

115=(2x^2)/(1.00-x)(2.00-x)

We move all terms to the left:

115-((2x^2)/(1.00-x)(2.00-x))=0


Domain of the equation: (1.00-x)(2.00-x))!=0

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

-x)(2.00-x)!=-1.00

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

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

We multiply parentheses

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

We add all the numbers together, and all the variables

117x^2-345x+230

Back to the equation:

-(117x^2-345x+230)


We get rid of parentheses

-117x^2+345x-230=0

a = -117; b = 345; c = -230;
Δ = b2-4ac
Δ = 3452-4·(-117)·(-230)
Δ = 11385
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:

$\sqrt{\Delta}=\sqrt{11385}=\sqrt{9*1265}=\sqrt{9}*\sqrt{1265}=3\sqrt{1265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(345)-3\sqrt{1265}}{2*-117}=\frac{-345-3\sqrt{1265}}{-234}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(345)+3\sqrt{1265}}{2*-117}=\frac{-345+3\sqrt{1265}}{-234}
$