-80x+800-x^2-20x=0

Solution for -80x+800-x^2-20x=0 equation:

-80x+800-x^2-20x=0

We add all the numbers together, and all the variables

-1x^2-100x+800=0

a = -1; b = -100; c = +800;
Δ = b2-4ac
Δ = -1002-4·(-1)·800
Δ = 13200
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:

$\sqrt{\Delta}=\sqrt{13200}=\sqrt{400*33}=\sqrt{400}*\sqrt{33}=20\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{33}}{2*-1}=\frac{100-20\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{33}}{2*-1}=\frac{100+20\sqrt{33}}{-2}
$