H=52t-16t^2

Solution for H=52t-16t^2 equation:

=52H-16H^2

We move all terms to the left:

-(52H-16H^2)=0

We get rid of parentheses

16H^2-52H=0

a = 16; b = -52; c = 0;
Δ = b2-4ac
Δ = -522-4·16·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-52}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+52}{2*16}=\frac{104}{32}
=3+1/4
$