H(0)=-16t^2+65

Solution for H(0)=-16t^2+65 equation:

(0)=-16H^2+65

We move all terms to the left:

(0)-(-16H^2+65)=0

We add all the numbers together, and all the variables

-(-16H^2+65)=0

We get rid of parentheses

16H^2-65=0

a = 16; b = 0; c = -65;
Δ = b2-4ac
Δ = 02-4·16·(-65)
Δ = 4160
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:

$\sqrt{\Delta}=\sqrt{4160}=\sqrt{64*65}=\sqrt{64}*\sqrt{65}=8\sqrt{65}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{65}}{2*16}=\frac{0-8\sqrt{65}}{32}
=-\frac{8\sqrt{65}}{32}
=-\frac{\sqrt{65}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{65}}{2*16}=\frac{0+8\sqrt{65}}{32}
=\frac{8\sqrt{65}}{32}
=\frac{\sqrt{65}}{4}
$