S(t)=-16t2+100

Solution for S(t)=-16t2+100 equation:

(S)=-16S^2+100

We move all terms to the left:

(S)-(-16S^2+100)=0

We get rid of parentheses

16S^2+S-100=0

a = 16; b = 1; c = -100;
Δ = b2-4ac
Δ = 12-4·16·(-100)
Δ = 6401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{6401}}{2*16}=\frac{-1-\sqrt{6401}}{32}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{6401}}{2*16}=\frac{-1+\sqrt{6401}}{32}
$