H(t)=-16t^2+54t

Solution for H(t)=-16t^2+54t equation:

(H)=-16H^2+54H

We move all terms to the left:

(H)-(-16H^2+54H)=0

We get rid of parentheses

16H^2-54H+H=0

We add all the numbers together, and all the variables

16H^2-53H=0

a = 16; b = -53; c = 0;
Δ = b2-4ac
Δ = -532-4·16·0
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-53}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+53}{2*16}=\frac{106}{32}
=3+5/16
$