6c^2+63c-72=0

Solution for 6c^2+63c-72=0 equation:

6c^2+63c-72=0

a = 6; b = 63; c = -72;
Δ = b2-4ac
Δ = 632-4·6·(-72)
Δ = 5697
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:

$\sqrt{\Delta}=\sqrt{5697}=\sqrt{9*633}=\sqrt{9}*\sqrt{633}=3\sqrt{633}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{633}}{2*6}=\frac{-63-3\sqrt{633}}{12}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{633}}{2*6}=\frac{-63+3\sqrt{633}}{12}
$