S=-16t^2+64t+72

Solution for S=-16t^2+64t+72 equation:

=-16S^2+64S+72

We move all terms to the left:

-(-16S^2+64S+72)=0

We get rid of parentheses

16S^2-64S-72=0

a = 16; b = -64; c = -72;
Δ = b2-4ac
Δ = -642-4·16·(-72)
Δ = 8704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8704}=\sqrt{256*34}=\sqrt{256}*\sqrt{34}=16\sqrt{34}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{34}}{2*16}=\frac{64-16\sqrt{34}}{32}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{34}}{2*16}=\frac{64+16\sqrt{34}}{32}
$