4c^2-72=-24c

Solution for 4c^2-72=-24c equation:

4c^2-72=-24c

We move all terms to the left:

4c^2-72-(-24c)=0

We get rid of parentheses

4c^2+24c-72=0

a = 4; b = 24; c = -72;
Δ = b2-4ac
Δ = 242-4·4·(-72)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{3}}{2*4}=\frac{-24-24\sqrt{3}}{8}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{3}}{2*4}=\frac{-24+24\sqrt{3}}{8}
$