S(t)=-16t2+100t+20

Solution for S(t)=-16t2+100t+20 equation:

(S)=-16S^2+100S+20

We move all terms to the left:

(S)-(-16S^2+100S+20)=0

We get rid of parentheses

16S^2-100S+S-20=0

We add all the numbers together, and all the variables

16S^2-99S-20=0

a = 16; b = -99; c = -20;
Δ = b2-4ac
Δ = -992-4·16·(-20)
Δ = 11081
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{-(-99)-\sqrt{11081}}{2*16}=\frac{99-\sqrt{11081}}{32}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{11081}}{2*16}=\frac{99+\sqrt{11081}}{32}
$