2=-6c^2+8c+6

Solution for 2=-6c^2+8c+6 equation:

2=-6c^2+8c+6

We move all terms to the left:

2-(-6c^2+8c+6)=0

We get rid of parentheses

6c^2-8c-6+2=0

We add all the numbers together, and all the variables

6c^2-8c-4=0

a = 6; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·6·(-4)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{10}}{2*6}=\frac{8-4\sqrt{10}}{12}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*6}=\frac{8+4\sqrt{10}}{12}
$