12y^2-48y-156=0

Solution for 12y^2-48y-156=0 equation:

12y^2-48y-156=0

a = 12; b = -48; c = -156;
Δ = b2-4ac
Δ = -482-4·12·(-156)
Δ = 9792
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:

$\sqrt{\Delta}=\sqrt{9792}=\sqrt{576*17}=\sqrt{576}*\sqrt{17}=24\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{17}}{2*12}=\frac{48-24\sqrt{17}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{17}}{2*12}=\frac{48+24\sqrt{17}}{24}
$