H=-16t^2+44t-9

Solution for H=-16t^2+44t-9 equation:

=-16H^2+44H-9

We move all terms to the left:

-(-16H^2+44H-9)=0

We get rid of parentheses

16H^2-44H+9=0

a = 16; b = -44; c = +9;
Δ = b2-4ac
Δ = -442-4·16·9
Δ = 1360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{85}}{2*16}=\frac{44-4\sqrt{85}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{85}}{2*16}=\frac{44+4\sqrt{85}}{32}
$