S(t)=-16t^2+40t+70

Solution for S(t)=-16t^2+40t+70 equation:

(S)=-16S^2+40S+70

We move all terms to the left:

(S)-(-16S^2+40S+70)=0

We get rid of parentheses

16S^2-40S+S-70=0

We add all the numbers together, and all the variables

16S^2-39S-70=0

a = 16; b = -39; c = -70;
Δ = b2-4ac
Δ = -392-4·16·(-70)
Δ = 6001
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{-(-39)-\sqrt{6001}}{2*16}=\frac{39-\sqrt{6001}}{32}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{6001}}{2*16}=\frac{39+\sqrt{6001}}{32}
$