H=-16t^2+72+100

Solution for H=-16t^2+72+100 equation:

=-16H^2+72+100

We move all terms to the left:

-(-16H^2+72+100)=0

We get rid of parentheses

16H^2-72-100=0

We add all the numbers together, and all the variables

16H^2-172=0

a = 16; b = 0; c = -172;
Δ = b2-4ac
Δ = 02-4·16·(-172)
Δ = 11008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11008}=\sqrt{256*43}=\sqrt{256}*\sqrt{43}=16\sqrt{43}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{43}}{2*16}=\frac{0-16\sqrt{43}}{32}
=-\frac{16\sqrt{43}}{32}
=-\frac{\sqrt{43}}{2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{43}}{2*16}=\frac{0+16\sqrt{43}}{32}
=\frac{16\sqrt{43}}{32}
=\frac{\sqrt{43}}{2}
$