3(c-2)c=8

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

3(c-2)c=8

We move all terms to the left:

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

We multiply parentheses

3c^2-6c-8=0

a = 3; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·3·(-8)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{33}}{2*3}=\frac{6-2\sqrt{33}}{6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{33}}{2*3}=\frac{6+2\sqrt{33}}{6}
$