12c^2+6c=81

Solution for 12c^2+6c=81 equation:

12c^2+6c=81

We move all terms to the left:

12c^2+6c-(81)=0

a = 12; b = 6; c = -81;
Δ = b2-4ac
Δ = 62-4·12·(-81)
Δ = 3924
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:

$\sqrt{\Delta}=\sqrt{3924}=\sqrt{36*109}=\sqrt{36}*\sqrt{109}=6\sqrt{109}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{109}}{2*12}=\frac{-6-6\sqrt{109}}{24}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{109}}{2*12}=\frac{-6+6\sqrt{109}}{24}
$