3(c+6)c=4

Solution for 3(c+6)c=4 equation:

3(c+6)c=4

We move all terms to the left:

3(c+6)c-(4)=0

We multiply parentheses

3c^2+18c-4=0

a = 3; b = 18; c = -4;
Δ = b2-4ac
Δ = 182-4·3·(-4)
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*3}=\frac{-18-2\sqrt{93}}{6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{93}}{2*3}=\frac{-18+2\sqrt{93}}{6}
$