(x-20)(x-20)=100

Solution for (x-20)(x-20)=100 equation:

(x-20)(x-20)=100

We move all terms to the left:

(x-20)(x-20)-(100)=0

We multiply parentheses ..

(+x^2-20x-20x+400)-100=0

We get rid of parentheses

x^2-20x-20x+400-100=0

We add all the numbers together, and all the variables

x^2-40x+300=0

a = 1; b = -40; c = +300;
Δ = b2-4ac
Δ = -402-4·1·300
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20}{2*1}=\frac{20}{2}
=10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20}{2*1}=\frac{60}{2}
=30
$