180-(2x+2)(x+10)=x

Solution for 180-(2x+2)(x+10)=x equation:

180-(2x+2)(x+10)=x

We move all terms to the left:

180-(2x+2)(x+10)-(x)=0

We add all the numbers together, and all the variables

-1x-(2x+2)(x+10)+180=0

We multiply parentheses ..

-(+2x^2+20x+2x+20)-1x+180=0

We get rid of parentheses

-2x^2-20x-2x-1x-20+180=0

We add all the numbers together, and all the variables

-2x^2-23x+160=0

a = -2; b = -23; c = +160;
Δ = b2-4ac
Δ = -232-4·(-2)·160
Δ = 1809
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:

$\sqrt{\Delta}=\sqrt{1809}=\sqrt{9*201}=\sqrt{9}*\sqrt{201}=3\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-3\sqrt{201}}{2*-2}=\frac{23-3\sqrt{201}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+3\sqrt{201}}{2*-2}=\frac{23+3\sqrt{201}}{-4}
$