H=-16t^2+54t+6

Solution for H=-16t^2+54t+6 equation:

=-16H^2+54H+6

We move all terms to the left:

-(-16H^2+54H+6)=0

We get rid of parentheses

16H^2-54H-6=0

a = 16; b = -54; c = -6;
Δ = b2-4ac
Δ = -542-4·16·(-6)
Δ = 3300
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:

$\sqrt{\Delta}=\sqrt{3300}=\sqrt{100*33}=\sqrt{100}*\sqrt{33}=10\sqrt{33}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-10\sqrt{33}}{2*16}=\frac{54-10\sqrt{33}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+10\sqrt{33}}{2*16}=\frac{54+10\sqrt{33}}{32}
$