H=5+46.3t-16t^2

Solution for H=5+46.3t-16t^2 equation:

=5+46.3H-16H^2

We move all terms to the left:

-(5+46.3H-16H^2)=0

We get rid of parentheses

16H^2-46.3H-5=0

a = 16; b = -46.3; c = -5;
Δ = b2-4ac
Δ = -46.32-4·16·(-5)
Δ = 2463.69
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{-(-46.3)-\sqrt{2463.69}}{2*16}=\frac{46.3-\sqrt{2463.69}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46.3)+\sqrt{2463.69}}{2*16}=\frac{46.3+\sqrt{2463.69}}{32}
$