100=x(500-x)

Solution for 100=x(500-x) equation:

100=x(500-x)

We move all terms to the left:

100-(x(500-x))=0

We add all the numbers together, and all the variables

-(x(-1x+500))+100=0


We calculate terms in parentheses: -(x(-1x+500)), so:

x(-1x+500)

We multiply parentheses

-1x^2+500x

Back to the equation:

-(-1x^2+500x)


We get rid of parentheses

1x^2-500x+100=0

We add all the numbers together, and all the variables

x^2-500x+100=0

a = 1; b = -500; c = +100;
Δ = b2-4ac
Δ = -5002-4·1·100
Δ = 249600
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:

$\sqrt{\Delta}=\sqrt{249600}=\sqrt{6400*39}=\sqrt{6400}*\sqrt{39}=80\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-80\sqrt{39}}{2*1}=\frac{500-80\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+80\sqrt{39}}{2*1}=\frac{500+80\sqrt{39}}{2}
$