X(15+x)=500

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

X(15+X)=500

We move all terms to the left:

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

We add all the numbers together, and all the variables

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}
$