H(t)=-16t^2+73t+6

Solution for H(t)=-16t^2+73t+6 equation:

(H)=-16H^2+73H+6

We move all terms to the left:

(H)-(-16H^2+73H+6)=0

We get rid of parentheses

16H^2-73H+H-6=0

We add all the numbers together, and all the variables

16H^2-72H-6=0

a = 16; b = -72; c = -6;
Δ = b2-4ac
Δ = -722-4·16·(-6)
Δ = 5568
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:

$\sqrt{\Delta}=\sqrt{5568}=\sqrt{64*87}=\sqrt{64}*\sqrt{87}=8\sqrt{87}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{87}}{2*16}=\frac{72-8\sqrt{87}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{87}}{2*16}=\frac{72+8\sqrt{87}}{32}
$