3y^2-12y-108=0

Solution for 3y^2-12y-108=0 equation:

3y^2-12y-108=0

a = 3; b = -12; c = -108;
Δ = b2-4ac
Δ = -122-4·3·(-108)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{10}}{2*3}=\frac{12-12\sqrt{10}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{10}}{2*3}=\frac{12+12\sqrt{10}}{6}
$