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

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

(S)=5S^2-80S

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5S^2+81S=0

a = -5; b = 81; c = 0;
Δ = b2-4ac
Δ = 812-4·(-5)·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-81}{2*-5}=\frac{-162}{-10}
=16+1/5
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+81}{2*-5}=\frac{0}{-10}
=0
$