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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

16H^2-23H-16=0

a = 16; b = -23; c = -16;
Δ = b2-4ac
Δ = -232-4·16·(-16)
Δ = 1553
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{1553}}{2*16}=\frac{23-\sqrt{1553}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{1553}}{2*16}=\frac{23+\sqrt{1553}}{32}
$