6x^2-18x-108=8

Solution for 6x^2-18x-108=8 equation:

6x^2-18x-108=8

We move all terms to the left:

6x^2-18x-108-(8)=0

We add all the numbers together, and all the variables

6x^2-18x-116=0

a = 6; b = -18; c = -116;
Δ = b2-4ac
Δ = -182-4·6·(-116)
Δ = 3108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3108}=\sqrt{4*777}=\sqrt{4}*\sqrt{777}=2\sqrt{777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{777}}{2*6}=\frac{18-2\sqrt{777}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{777}}{2*6}=\frac{18+2\sqrt{777}}{12}
$