0=-8x^2+80x+500

Solution for 0=-8x^2+80x+500 equation:

0=-8x^2+80x+500

We move all terms to the left:

0-(-8x^2+80x+500)=0

We add all the numbers together, and all the variables

-(-8x^2+80x+500)=0

We get rid of parentheses

8x^2-80x-500=0

a = 8; b = -80; c = -500;
Δ = b2-4ac
Δ = -802-4·8·(-500)
Δ = 22400
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:

$\sqrt{\Delta}=\sqrt{22400}=\sqrt{1600*14}=\sqrt{1600}*\sqrt{14}=40\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-40\sqrt{14}}{2*8}=\frac{80-40\sqrt{14}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+40\sqrt{14}}{2*8}=\frac{80+40\sqrt{14}}{16}
$