S=25t-2.5t^2

Solution for S=25t-2.5t^2 equation:

=25S-2.5S^2

We move all terms to the left:

-(25S-2.5S^2)=0

We get rid of parentheses

2.5S^2-25S=0

a = 2.5; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·2.5·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*2.5}=\frac{0}{5}
=0
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*2.5}=\frac{50}{5}
=10
$