H(t)=-4.9t^2+22t+5.5

Solution for H(t)=-4.9t^2+22t+5.5 equation:

(H)=-4.9H^2+22H+5.5

We move all terms to the left:

(H)-(-4.9H^2+22H+5.5)=0

We get rid of parentheses

4.9H^2-22H+H-5.5=0

We add all the numbers together, and all the variables

4.9H^2-21H-5.5=0

a = 4.9; b = -21; c = -5.5;
Δ = b2-4ac
Δ = -212-4·4.9·(-5.5)
Δ = 548.8
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{-(-21)-\sqrt{548.8}}{2*4.9}=\frac{21-\sqrt{548.8}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{548.8}}{2*4.9}=\frac{21+\sqrt{548.8}}{9.8}
$