H=-0.55t^2+16.5t

Solution for H=-0.55t^2+16.5t equation:

=-0.55H^2+16.5H

We move all terms to the left:

-(-0.55H^2+16.5H)=0

We get rid of parentheses

0.55H^2-16.5H=0

a = 0.55; b = -16.5; c = 0;
Δ = b2-4ac
Δ = -16.52-4·0.55·0
Δ = 272.25
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{-(-16.5)-\sqrt{272.25}}{2*0.55}=\frac{16.5-\sqrt{272.25}}{1.1}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16.5)+\sqrt{272.25}}{2*0.55}=\frac{16.5+\sqrt{272.25}}{1.1}
$