H=6+61t-16t^2

Solution for H=6+61t-16t^2 equation:

=6+61H-16H^2

We move all terms to the left:

-(6+61H-16H^2)=0

We get rid of parentheses

16H^2-61H-6=0

a = 16; b = -61; c = -6;
Δ = b2-4ac
Δ = -612-4·16·(-6)
Δ = 4105
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{4105}}{2*16}=\frac{61-\sqrt{4105}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+\sqrt{4105}}{2*16}=\frac{61+\sqrt{4105}}{32}
$