H=204t-16t^2

Solution for H=204t-16t^2 equation:

=204H-16H^2

We move all terms to the left:

-(204H-16H^2)=0

We get rid of parentheses

16H^2-204H=0

a = 16; b = -204; c = 0;
Δ = b2-4ac
Δ = -2042-4·16·0
Δ = 41616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{41616}=204$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-204}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+204}{2*16}=\frac{408}{32}
=12+3/4
$