6a^2-36a-108=0

Solution for 6a^2-36a-108=0 equation:

6a^2-36a-108=0

a = 6; b = -36; c = -108;
Δ = b2-4ac
Δ = -362-4·6·(-108)
Δ = 3888
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36\sqrt{3}}{2*6}=\frac{36-36\sqrt{3}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36\sqrt{3}}{2*6}=\frac{36+36\sqrt{3}}{12}
$