-15x^2+120x+192=0

Solution for -15x^2+120x+192=0 equation:

-15x^2+120x+192=0

a = -15; b = 120; c = +192;
Δ = b2-4ac
Δ = 1202-4·(-15)·192
Δ = 25920
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:

$\sqrt{\Delta}=\sqrt{25920}=\sqrt{5184*5}=\sqrt{5184}*\sqrt{5}=72\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-72\sqrt{5}}{2*-15}=\frac{-120-72\sqrt{5}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+72\sqrt{5}}{2*-15}=\frac{-120+72\sqrt{5}}{-30}
$