X(50-x)=500

Solution for X(50-x)=500 equation:

X(50-X)=500

We move all terms to the left:

X(50-X)-(500)=0

We add all the numbers together, and all the variables

X(-1X+50)-500=0

We multiply parentheses

-1X^2+50X-500=0

a = -1; b = 50; c = -500;
Δ = b2-4ac
Δ = 502-4·(-1)·(-500)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{5}}{2*-1}=\frac{-50-10\sqrt{5}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{5}}{2*-1}=\frac{-50+10\sqrt{5}}{-2}
$