H=6+30t-16t^2

Solution for H=6+30t-16t^2 equation:

=6+30H-16H^2

We move all terms to the left:

-(6+30H-16H^2)=0

We get rid of parentheses

16H^2-30H-6=0

a = 16; b = -30; c = -6;
Δ = b2-4ac
Δ = -302-4·16·(-6)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{321}}{2*16}=\frac{30-2\sqrt{321}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{321}}{2*16}=\frac{30+2\sqrt{321}}{32}
$