x(x+15)-96=0

Solution for x(x+15)-96=0 equation:

x(x+15)-96=0

We multiply parentheses

x^2+15x-96=0

a = 1; b = 15; c = -96;
Δ = b2-4ac
Δ = 152-4·1·(-96)
Δ = 609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{609}}{2*1}=\frac{-15-\sqrt{609}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{609}}{2*1}=\frac{-15+\sqrt{609}}{2}
$