6x^2-12x-90=2

Solution for 6x^2-12x-90=2 equation:

6x^2-12x-90=2

We move all terms to the left:

6x^2-12x-90-(2)=0

We add all the numbers together, and all the variables

6x^2-12x-92=0

a = 6; b = -12; c = -92;
Δ = b2-4ac
Δ = -122-4·6·(-92)
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-28\sqrt{3}}{2*6}=\frac{12-28\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+28\sqrt{3}}{2*6}=\frac{12+28\sqrt{3}}{12}
$