(x+40)(x-20)=180

Solution for (x+40)(x-20)=180 equation:

(x+40)(x-20)=180

We move all terms to the left:

(x+40)(x-20)-(180)=0

We multiply parentheses ..

(+x^2-20x+40x-800)-180=0

We get rid of parentheses

x^2-20x+40x-800-180=0

We add all the numbers together, and all the variables

x^2+20x-980=0

a = 1; b = 20; c = -980;
Δ = b2-4ac
Δ = 202-4·1·(-980)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12\sqrt{30}}{2*1}=\frac{-20-12\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12\sqrt{30}}{2*1}=\frac{-20+12\sqrt{30}}{2}
$