H=38+16t-16t^2

Solution for H=38+16t-16t^2 equation:

=38+16H-16H^2

We move all terms to the left:

-(38+16H-16H^2)=0

We get rid of parentheses

16H^2-16H-38=0

a = 16; b = -16; c = -38;
Δ = b2-4ac
Δ = -162-4·16·(-38)
Δ = 2688
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{42}}{2*16}=\frac{16-8\sqrt{42}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{42}}{2*16}=\frac{16+8\sqrt{42}}{32}
$