H=6+50t-16t2

Solution for H=6+50t-16t2 equation:

=6+50H-16H^2

We move all terms to the left:

-(6+50H-16H^2)=0

We get rid of parentheses

16H^2-50H-6=0

a = 16; b = -50; c = -6;
Δ = b2-4ac
Δ = -502-4·16·(-6)
Δ = 2884
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:

$\sqrt{\Delta}=\sqrt{2884}=\sqrt{4*721}=\sqrt{4}*\sqrt{721}=2\sqrt{721}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{721}}{2*16}=\frac{50-2\sqrt{721}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{721}}{2*16}=\frac{50+2\sqrt{721}}{32}
$