x(x+15)=300

Solution for x(x+15)=300 equation:

x(x+15)=300

We move all terms to the left:

x(x+15)-(300)=0

We multiply parentheses

x^2+15x-300=0

a = 1; b = 15; c = -300;
Δ = b2-4ac
Δ = 152-4·1·(-300)
Δ = 1425
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:

$\sqrt{\Delta}=\sqrt{1425}=\sqrt{25*57}=\sqrt{25}*\sqrt{57}=5\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{57}}{2*1}=\frac{-15-5\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{57}}{2*1}=\frac{-15+5\sqrt{57}}{2}
$