H=-16t^2+59t+6

Solution for H=-16t^2+59t+6 equation:

=-16H^2+59H+6

We move all terms to the left:

-(-16H^2+59H+6)=0

We get rid of parentheses

16H^2-59H-6=0

a = 16; b = -59; c = -6;
Δ = b2-4ac
Δ = -592-4·16·(-6)
Δ = 3865
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{-(-59)-\sqrt{3865}}{2*16}=\frac{59-\sqrt{3865}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{3865}}{2*16}=\frac{59+\sqrt{3865}}{32}
$