H(t)=16t^2-100

Solution for H(t)=16t^2-100 equation:

(H)=16H^2-100

We move all terms to the left:

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

We get rid of parentheses

-16H^2+H+100=0

a = -16; b = 1; c = +100;
Δ = b2-4ac
Δ = 12-4·(-16)·100
Δ = 6401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{6401}}{2*-16}=\frac{-1-\sqrt{6401}}{-32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{6401}}{2*-16}=\frac{-1+\sqrt{6401}}{-32}
$