(x-18)(x-20)=180

Solution for (x-18)(x-20)=180 equation:

(x-18)(x-20)=180

We move all terms to the left:

(x-18)(x-20)-(180)=0

We multiply parentheses ..

(+x^2-20x-18x+360)-180=0

We get rid of parentheses

x^2-20x-18x+360-180=0

We add all the numbers together, and all the variables

x^2-38x+180=0

a = 1; b = -38; c = +180;
Δ = b2-4ac
Δ = -382-4·1·180
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{181}}{2*1}=\frac{38-2\sqrt{181}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{181}}{2*1}=\frac{38+2\sqrt{181}}{2}
$