S=-16t^2+88t+4

Solution for S=-16t^2+88t+4 equation:

=-16S^2+88S+4

We move all terms to the left:

-(-16S^2+88S+4)=0

We get rid of parentheses

16S^2-88S-4=0

a = 16; b = -88; c = -4;
Δ = b2-4ac
Δ = -882-4·16·(-4)
Δ = 8000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-40\sqrt{5}}{2*16}=\frac{88-40\sqrt{5}}{32}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+40\sqrt{5}}{2*16}=\frac{88+40\sqrt{5}}{32}
$