S=-16t^2+30+7

Solution for S=-16t^2+30+7 equation:

=-16S^2+30+7

We move all terms to the left:

-(-16S^2+30+7)=0

We get rid of parentheses

16S^2-30-7=0

We add all the numbers together, and all the variables

16S^2-37=0

a = 16; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·16·(-37)
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{37}}{2*16}=\frac{0-8\sqrt{37}}{32}
=-\frac{8\sqrt{37}}{32}
=-\frac{\sqrt{37}}{4}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{37}}{2*16}=\frac{0+8\sqrt{37}}{32}
=\frac{8\sqrt{37}}{32}
=\frac{\sqrt{37}}{4}
$