S=100+84t-14t^2

Solution for S=100+84t-14t^2 equation:

=100+84S-14S^2

We move all terms to the left:

-(100+84S-14S^2)=0

We get rid of parentheses

14S^2-84S-100=0

a = 14; b = -84; c = -100;
Δ = b2-4ac
Δ = -842-4·14·(-100)
Δ = 12656
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:

$\sqrt{\Delta}=\sqrt{12656}=\sqrt{16*791}=\sqrt{16}*\sqrt{791}=4\sqrt{791}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{791}}{2*14}=\frac{84-4\sqrt{791}}{28}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{791}}{2*14}=\frac{84+4\sqrt{791}}{28}
$