x(x-5)=500

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

x(x-5)=500

We move all terms to the left:

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
$