12(3x^2-2x-2)=0

Solution for 12(3x^2-2x-2)=0 equation:

12(3x^2-2x-2)=0

We multiply parentheses

36x^2-24x-24=0

a = 36; b = -24; c = -24;
Δ = b2-4ac
Δ = -242-4·36·(-24)
Δ = 4032
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:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{7}}{2*36}=\frac{24-24\sqrt{7}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{7}}{2*36}=\frac{24+24\sqrt{7}}{72}
$