3n^2-12n-132=0

Solution for 3n^2-12n-132=0 equation:

3n^2-12n-132=0

a = 3; b = -12; c = -132;
Δ = b2-4ac
Δ = -122-4·3·(-132)
Δ = 1728
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24\sqrt{3}}{2*3}=\frac{12-24\sqrt{3}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24\sqrt{3}}{2*3}=\frac{12+24\sqrt{3}}{6}
$