S(t)=-16t^2+80t+60

Solution for S(t)=-16t^2+80t+60 equation:

(S)=-16S^2+80S+60

We move all terms to the left:

(S)-(-16S^2+80S+60)=0

We get rid of parentheses

16S^2-80S+S-60=0

We add all the numbers together, and all the variables

16S^2-79S-60=0

a = 16; b = -79; c = -60;
Δ = b2-4ac
Δ = -792-4·16·(-60)
Δ = 10081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-\sqrt{10081}}{2*16}=\frac{79-\sqrt{10081}}{32}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+\sqrt{10081}}{2*16}=\frac{79+\sqrt{10081}}{32}
$