H=-16t^2+81

Solution for H=-16t^2+81 equation:

=-16H^2+81

We move all terms to the left:

-(-16H^2+81)=0

We get rid of parentheses

16H^2-81=0

a = 16; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·16·(-81)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*16}=\frac{-72}{32}
=-2+1/4
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*16}=\frac{72}{32}
=2+1/4
$