H(t)=-16(t^2-2.25)

Solution for H(t)=-16(t^2-2.25) equation:

(H)=-16(H^2-2.25)

We move all terms to the left:

(H)-(-16(H^2-2.25))=0


We calculate terms in parentheses: -(-16(H^2-2.25)), so:

-16(H^2-2.25)

We multiply parentheses

-16H^2+36

Back to the equation:

-(-16H^2+36)


We get rid of parentheses

16H^2+H-36=0

a = 16; b = 1; c = -36;
Δ = b2-4ac
Δ = 12-4·16·(-36)
Δ = 2305
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{-(1)-\sqrt{2305}}{2*16}=\frac{-1-\sqrt{2305}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2305}}{2*16}=\frac{-1+\sqrt{2305}}{32}
$