S=-5t^2+80t

Solution for S=-5t^2+80t equation:

=-5S^2+80S

We move all terms to the left:

-(-5S^2+80S)=0

We get rid of parentheses

5S^2-80S=0

a = 5; b = -80; c = 0;
Δ = b2-4ac
Δ = -802-4·5·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-80}{2*5}=\frac{0}{10}
=0
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+80}{2*5}=\frac{160}{10}
=16
$