H=5+9t-16t^2

Solution for H=5+9t-16t^2 equation:

=5+9H-16H^2

We move all terms to the left:

-(5+9H-16H^2)=0

We get rid of parentheses

16H^2-9H-5=0

a = 16; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·16·(-5)
Δ = 401
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{-(-9)-\sqrt{401}}{2*16}=\frac{9-\sqrt{401}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{401}}{2*16}=\frac{9+\sqrt{401}}{32}
$