X(x-15)=500

Solution for X(x-15)=500 equation:

X(X-15)=500

We move all terms to the left:

X(X-15)-(500)=0

We multiply parentheses

X^2-15X-500=0

a = 1; b = -15; c = -500;
Δ = b2-4ac
Δ = -152-4·1·(-500)
Δ = 2225
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:

$\sqrt{\Delta}=\sqrt{2225}=\sqrt{25*89}=\sqrt{25}*\sqrt{89}=5\sqrt{89}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{89}}{2*1}=\frac{15-5\sqrt{89}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{89}}{2*1}=\frac{15+5\sqrt{89}}{2}
$