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

Solution for 2(x^2-2x)+20=180 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

2(x^2-2x)-160=0

We multiply parentheses

2x^2-4x-160=0

a = 2; b = -4; c = -160;
Δ = b2-4ac
Δ = -42-4·2·(-160)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-36}{2*2}=\frac{-32}{4}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+36}{2*2}=\frac{40}{4}
=10
$