(x+20)(x-10)=180

Solution for (x+20)(x-10)=180 equation:

(x+20)(x-10)=180

We move all terms to the left:

(x+20)(x-10)-(180)=0

We multiply parentheses ..

(+x^2-10x+20x-200)-180=0

We get rid of parentheses

x^2-10x+20x-200-180=0

We add all the numbers together, and all the variables

x^2+10x-380=0

a = 1; b = 10; c = -380;
Δ = b2-4ac
Δ = 102-4·1·(-380)
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-18\sqrt{5}}{2*1}=\frac{-10-18\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+18\sqrt{5}}{2*1}=\frac{-10+18\sqrt{5}}{2}
$