S(t)=80t-5t2

Solution for S(t)=80t-5t2 equation:

(S)=80S-5S^2

We move all terms to the left:

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

We get rid of parentheses

5S^2-80S+S=0

We add all the numbers together, and all the variables

5S^2-79S=0

a = 5; b = -79; c = 0;
Δ = b2-4ac
Δ = -792-4·5·0
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-79}{2*5}=\frac{0}{10}
=0
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+79}{2*5}=\frac{158}{10}
=15+4/5
$