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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-16S^2-63S-16=0

a = -16; b = -63; c = -16;
Δ = b2-4ac
Δ = -632-4·(-16)·(-16)
Δ = 2945
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{2945}}{2*-16}=\frac{63-\sqrt{2945}}{-32}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{2945}}{2*-16}=\frac{63+\sqrt{2945}}{-32}
$