H(t)=-16t2+40t+5.5.

Solution for H(t)=-16t2+40t+5.5. equation:

(H)=-16H^2+40H+5.5.

We move all terms to the left:

(H)-(-16H^2+40H+5.5.)=0

We get rid of parentheses

16H^2-40H+H-5.5.=0

We add all the numbers together, and all the variables

16H^2-39H=0

a = 16; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·16·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*16}=\frac{78}{32}
=2+7/16
$