S(t)=-16t^2+64t+100

Solution for S(t)=-16t^2+64t+100 equation:

(S)=-16S^2+64S+100

We move all terms to the left:

(S)-(-16S^2+64S+100)=0

We get rid of parentheses

16S^2-64S+S-100=0

We add all the numbers together, and all the variables

16S^2-63S-100=0

a = 16; b = -63; c = -100;
Δ = b2-4ac
Δ = -632-4·16·(-100)
Δ = 10369
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{-(-63)-\sqrt{10369}}{2*16}=\frac{63-\sqrt{10369}}{32}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{10369}}{2*16}=\frac{63+\sqrt{10369}}{32}
$