H=-16t^2+61t+8

Solution for H=-16t^2+61t+8 equation:

=-16H^2+61H+8

We move all terms to the left:

-(-16H^2+61H+8)=0

We get rid of parentheses

16H^2-61H-8=0

a = 16; b = -61; c = -8;
Δ = b2-4ac
Δ = -612-4·16·(-8)
Δ = 4233
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{-(-61)-\sqrt{4233}}{2*16}=\frac{61-\sqrt{4233}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+\sqrt{4233}}{2*16}=\frac{61+\sqrt{4233}}{32}
$