H=6+24t-16t^2

Solution for H=6+24t-16t^2 equation:

=6+24H-16H^2

We move all terms to the left:

-(6+24H-16H^2)=0

We get rid of parentheses

16H^2-24H-6=0

a = 16; b = -24; c = -6;
Δ = b2-4ac
Δ = -242-4·16·(-6)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{15}}{2*16}=\frac{24-8\sqrt{15}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{15}}{2*16}=\frac{24+8\sqrt{15}}{32}
$