6(c-3)c=2

Solution for 6(c-3)c=2 equation:

6(c-3)c=2

We move all terms to the left:

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

We multiply parentheses

6c^2-18c-2=0

a = 6; b = -18; c = -2;
Δ = b2-4ac
Δ = -182-4·6·(-2)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*6}=\frac{18-2\sqrt{93}}{12}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*6}=\frac{18+2\sqrt{93}}{12}
$