6x^2-2x-12=-2

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

6x^2-2x-12=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

6x^2-2x-10=0

a = 6; b = -2; c = -10;
Δ = b2-4ac
Δ = -22-4·6·(-10)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{61}}{2*6}=\frac{2-2\sqrt{61}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{61}}{2*6}=\frac{2+2\sqrt{61}}{12}
$