H(t)=-16t^2+24t+9

Solution for H(t)=-16t^2+24t+9 equation:

(H)=-16H^2+24H+9

We move all terms to the left:

(H)-(-16H^2+24H+9)=0

We get rid of parentheses

16H^2-24H+H-9=0

We add all the numbers together, and all the variables

16H^2-23H-9=0

a = 16; b = -23; c = -9;
Δ = b2-4ac
Δ = -232-4·16·(-9)
Δ = 1105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{1105}}{2*16}=\frac{23-\sqrt{1105}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{1105}}{2*16}=\frac{23+\sqrt{1105}}{32}
$