x^2-20x-5=-80

Solution for x^2-20x-5=-80 equation:

x^2-20x-5=-80

We move all terms to the left:

x^2-20x-5-(-80)=0

We add all the numbers together, and all the variables

x^2-20x+75=0

a = 1; b = -20; c = +75;
Δ = b2-4ac
Δ = -202-4·1·75
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10}{2*1}=\frac{10}{2}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10}{2*1}=\frac{30}{2}
=15
$