20000=-x(500-2x)

Solution for 20000=-x(500-2x) equation:

20000=-x(500-2x)

We move all terms to the left:

20000-(-x(500-2x))=0

We add all the numbers together, and all the variables

-(-x(-2x+500))+20000=0


We calculate terms in parentheses: -(-x(-2x+500)), so:

-x(-2x+500)

We multiply parentheses

2x^2-500x

Back to the equation:

-(2x^2-500x)


We get rid of parentheses

-2x^2+500x+20000=0

a = -2; b = 500; c = +20000;
Δ = b2-4ac
Δ = 5002-4·(-2)·20000
Δ = 410000
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:

$\sqrt{\Delta}=\sqrt{410000}=\sqrt{10000*41}=\sqrt{10000}*\sqrt{41}=100\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-100\sqrt{41}}{2*-2}=\frac{-500-100\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+100\sqrt{41}}{2*-2}=\frac{-500+100\sqrt{41}}{-4}
$