S=12t-4.9t^2

Solution for S=12t-4.9t^2 equation:

=12S-4.9S^2

We move all terms to the left:

-(12S-4.9S^2)=0

We get rid of parentheses

4.9S^2-12S=0

a = 4.9; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·4.9·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*4.9}=\frac{0}{9.8}
=0
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*4.9}=\frac{24}{9.8}
=2+3.1428571428571/7
$