S=96+80t-16t2

Solution for S=96+80t-16t2 equation:

=96+80S-16S^2

We move all terms to the left:

-(96+80S-16S^2)=0

We get rid of parentheses

16S^2-80S-96=0

a = 16; b = -80; c = -96;
Δ = b2-4ac
Δ = -802-4·16·(-96)
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-112}{2*16}=\frac{-32}{32}
=-1
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+112}{2*16}=\frac{192}{32}
=6
$