H=6+32t-16t^2

Solution for H=6+32t-16t^2 equation:

=6+32H-16H^2

We move all terms to the left:

-(6+32H-16H^2)=0

We get rid of parentheses

16H^2-32H-6=0

a = 16; b = -32; c = -6;
Δ = b2-4ac
Δ = -322-4·16·(-6)
Δ = 1408
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:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{22}}{2*16}=\frac{32-8\sqrt{22}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{22}}{2*16}=\frac{32+8\sqrt{22}}{32}
$