H=6+29t+-16t^2

Solution for H=6+29t+-16t^2 equation:

=6+29H+-16H^2

We move all terms to the left:

-(6+29H+-16H^2)=0

We use the square of the difference formula

-(6+29H-16H^2)=0

We get rid of parentheses

16H^2-29H-6=0

a = 16; b = -29; c = -6;
Δ = b2-4ac
Δ = -292-4·16·(-6)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-35}{2*16}=\frac{-6}{32}
=-3/16
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+35}{2*16}=\frac{64}{32}
=2
$