H(t)=-4.9t^2+9.8t+2

Solution for H(t)=-4.9t^2+9.8t+2 equation:

(H)=-4.9H^2+9.8H+2

We move all terms to the left:

(H)-(-4.9H^2+9.8H+2)=0

We get rid of parentheses

4.9H^2-9.8H+H-2=0

We add all the numbers together, and all the variables

4.9H^2-8.8H-2=0

a = 4.9; b = -8.8; c = -2;
Δ = b2-4ac
Δ = -8.82-4·4.9·(-2)
Δ = 116.64
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{-(-8.8)-\sqrt{116.64}}{2*4.9}=\frac{8.8-\sqrt{116.64}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.8)+\sqrt{116.64}}{2*4.9}=\frac{8.8+\sqrt{116.64}}{9.8}
$