-12y^2+120y-120=0

Solution for -12y^2+120y-120=0 equation:

-12y^2+120y-120=0

a = -12; b = 120; c = -120;
Δ = b2-4ac
Δ = 1202-4·(-12)·(-120)
Δ = 8640
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8640}=\sqrt{576*15}=\sqrt{576}*\sqrt{15}=24\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-24\sqrt{15}}{2*-12}=\frac{-120-24\sqrt{15}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+24\sqrt{15}}{2*-12}=\frac{-120+24\sqrt{15}}{-24}
$