(2x-2)(x+5)+90=180

Solution for (2x-2)(x+5)+90=180 equation:

(2x-2)(x+5)+90=180

We move all terms to the left:

(2x-2)(x+5)+90-(180)=0

We add all the numbers together, and all the variables

(2x-2)(x+5)-90=0

We multiply parentheses ..

(+2x^2+10x-2x-10)-90=0

We get rid of parentheses

2x^2+10x-2x-10-90=0

We add all the numbers together, and all the variables

2x^2+8x-100=0

a = 2; b = 8; c = -100;
Δ = b2-4ac
Δ = 82-4·2·(-100)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{6}}{2*2}=\frac{-8-12\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{6}}{2*2}=\frac{-8+12\sqrt{6}}{4}
$