H=7+34t-16t^2

Solution for H=7+34t-16t^2 equation:

=7+34H-16H^2

We move all terms to the left:

-(7+34H-16H^2)=0

We get rid of parentheses

16H^2-34H-7=0

a = 16; b = -34; c = -7;
Δ = b2-4ac
Δ = -342-4·16·(-7)
Δ = 1604
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:

$\sqrt{\Delta}=\sqrt{1604}=\sqrt{4*401}=\sqrt{4}*\sqrt{401}=2\sqrt{401}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{401}}{2*16}=\frac{34-2\sqrt{401}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{401}}{2*16}=\frac{34+2\sqrt{401}}{32}
$