(3c^2)-2c-2=8

Solution for (3c^2)-2c-2=8 equation:

(3c^2)-2c-2=8

We move all terms to the left:

(3c^2)-2c-2-(8)=0

We add all the numbers together, and all the variables

3c^2-2c-10=0

a = 3; b = -2; c = -10;
Δ = b2-4ac
Δ = -22-4·3·(-10)
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*3}=\frac{2-2\sqrt{31}}{6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*3}=\frac{2+2\sqrt{31}}{6}
$