x(x-20)=80

Solution for x(x-20)=80 equation:

x(x-20)=80

We move all terms to the left:

x(x-20)-(80)=0

We multiply parentheses

x^2-20x-80=0

a = 1; b = -20; c = -80;
Δ = b2-4ac
Δ = -202-4·1·(-80)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-12\sqrt{5}}{2*1}=\frac{20-12\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+12\sqrt{5}}{2*1}=\frac{20+12\sqrt{5}}{2}
$