S=40t-0.8t^2

Solution for S=40t-0.8t^2 equation:

=40S-0.8S^2

We move all terms to the left:

-(40S-0.8S^2)=0

We get rid of parentheses

0.8S^2-40S=0

a = 0.8; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·0.8·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*0.8}=\frac{0}{1.6}
=0
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*0.8}=\frac{80}{1.6}
=50
$