S=80+64t-16t^2=0

Solution for S=80+64t-16t^2=0 equation:

=80+64S-16S^2=0

We move all terms to the left:

-(80+64S-16S^2)=0

We get rid of parentheses

16S^2-64S-80=0

a = 16; b = -64; c = -80;
Δ = b2-4ac
Δ = -642-4·16·(-80)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-96}{2*16}=\frac{-32}{32}
=-1
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+96}{2*16}=\frac{160}{32}
=5
$