x(x-15)=125

Solution for x(x-15)=125 equation:

x(x-15)=125

We move all terms to the left:

x(x-15)-(125)=0

We multiply parentheses

x^2-15x-125=0

a = 1; b = -15; c = -125;
Δ = b2-4ac
Δ = -152-4·1·(-125)
Δ = 725
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:

$\sqrt{\Delta}=\sqrt{725}=\sqrt{25*29}=\sqrt{25}*\sqrt{29}=5\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{29}}{2*1}=\frac{15-5\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{29}}{2*1}=\frac{15+5\sqrt{29}}{2}
$