H=16t^2+4.5t

Solution for H=16t^2+4.5t equation:

=16H^2+4.5H

We move all terms to the left:

-(16H^2+4.5H)=0

We get rid of parentheses

-16H^2-4.5H=0

a = -16; b = -4.5; c = 0;
Δ = b2-4ac
Δ = -4.52-4·(-16)·0
Δ = 20.25
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{-(-4.5)-\sqrt{20.25}}{2*-16}=\frac{4.5-\sqrt{20.25}}{-32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.5)+\sqrt{20.25}}{2*-16}=\frac{4.5+\sqrt{20.25}}{-32}
$