H(t)=-4.9t^2+24.55+1.5

Solution for H(t)=-4.9t^2+24.55+1.5 equation:

(H)=-4.9H^2+24.55+1.5

We move all terms to the left:

(H)-(-4.9H^2+24.55+1.5)=0

We get rid of parentheses

4.9H^2+H-24.55-1.5=0

We add all the numbers together, and all the variables

4.9H^2+H-26.05=0

a = 4.9; b = 1; c = -26.05;
Δ = b2-4ac
Δ = 12-4·4.9·(-26.05)
Δ = 511.58
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{511.58}}{2*4.9}=\frac{-1-\sqrt{511.58}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{511.58}}{2*4.9}=\frac{-1+\sqrt{511.58}}{9.8}
$