S=-16t^2+80t+576

Solution for S=-16t^2+80t+576 equation:

=-16S^2+80S+576

We move all terms to the left:

-(-16S^2+80S+576)=0

We get rid of parentheses

16S^2-80S-576=0

a = 16; b = -80; c = -576;
Δ = b2-4ac
Δ = -802-4·16·(-576)
Δ = 43264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{43264}=208$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-208}{2*16}=\frac{-128}{32}
=-4
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+208}{2*16}=\frac{288}{32}
=9
$