S=20-0.75t^2

Solution for S=20-0.75t^2 equation:

=20-0.75S^2

We move all terms to the left:

-(20-0.75S^2)=0

We get rid of parentheses

0.75S^2-20=0

a = 0.75; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·0.75·(-20)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*0.75}=\frac{0-2\sqrt{15}}{1.5}
=-\frac{2\sqrt{15}}{1.5}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*0.75}=\frac{0+2\sqrt{15}}{1.5}
=\frac{2\sqrt{15}}{1.5}
$