(x+20)(2x-20)=120

Solution for (x+20)(2x-20)=120 equation:

(x+20)(2x-20)=120

We move all terms to the left:

(x+20)(2x-20)-(120)=0

We multiply parentheses ..

(+2x^2-20x+40x-400)-120=0

We get rid of parentheses

2x^2-20x+40x-400-120=0

We add all the numbers together, and all the variables

2x^2+20x-520=0

a = 2; b = 20; c = -520;
Δ = b2-4ac
Δ = 202-4·2·(-520)
Δ = 4560
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:

$\sqrt{\Delta}=\sqrt{4560}=\sqrt{16*285}=\sqrt{16}*\sqrt{285}=4\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{285}}{2*2}=\frac{-20-4\sqrt{285}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{285}}{2*2}=\frac{-20+4\sqrt{285}}{4}
$