500=x(8-0.02x)

Solution for 500=x(8-0.02x) equation:

500=x(8-0.02x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(x(-0.02x+8))+500=0


We calculate terms in parentheses: -(x(-0.02x+8)), so:

x(-0.02x+8)

We multiply parentheses

0x^2+8x

We add all the numbers together, and all the variables

x^2+8x

Back to the equation:

-(x^2+8x)


We get rid of parentheses

-x^2-8x+500=0

We add all the numbers together, and all the variables

-1x^2-8x+500=0

a = -1; b = -8; c = +500;
Δ = b2-4ac
Δ = -82-4·(-1)·500
Δ = 2064
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:

$\sqrt{\Delta}=\sqrt{2064}=\sqrt{16*129}=\sqrt{16}*\sqrt{129}=4\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{129}}{2*-1}=\frac{8-4\sqrt{129}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{129}}{2*-1}=\frac{8+4\sqrt{129}}{-2}
$