500=8x-0.02x^2

Solution for 500=8x-0.02x^2 equation:

500=8x-0.02x^2

We move all terms to the left:

500-(8x-0.02x^2)=0

We get rid of parentheses

0.02x^2-8x+500=0

a = 0.02; b = -8; c = +500;
Δ = b2-4ac
Δ = -82-4·0.02·500
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{6}}{2*0.02}=\frac{8-2\sqrt{6}}{0.04}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{6}}{2*0.02}=\frac{8+2\sqrt{6}}{0.04}
$