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

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

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

We move all terms to the left:

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

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

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 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}
$