H=-16t^2+110t+4

Solution for H=-16t^2+110t+4 equation:

=-16H^2+110H+4

We move all terms to the left:

-(-16H^2+110H+4)=0

We get rid of parentheses

16H^2-110H-4=0

a = 16; b = -110; c = -4;
Δ = b2-4ac
Δ = -1102-4·16·(-4)
Δ = 12356
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:

$\sqrt{\Delta}=\sqrt{12356}=\sqrt{4*3089}=\sqrt{4}*\sqrt{3089}=2\sqrt{3089}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{3089}}{2*16}=\frac{110-2\sqrt{3089}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{3089}}{2*16}=\frac{110+2\sqrt{3089}}{32}
$