X(x-5)-500=0

Solution for X(x-5)-500=0 equation:

X(X-5)-500=0

We multiply parentheses

X^2-5X-500=0

a = 1; b = -5; c = -500;
Δ = b2-4ac
Δ = -52-4·1·(-500)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-45}{2*1}=\frac{-40}{2}
=-20
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+45}{2*1}=\frac{50}{2}
=25
$