H(t)=-4.9t^2+27.5t+8.9

Solution for H(t)=-4.9t^2+27.5t+8.9 equation:

(H)=-4.9H^2+27.5H+8.9

We move all terms to the left:

(H)-(-4.9H^2+27.5H+8.9)=0

We get rid of parentheses

4.9H^2-27.5H+H-8.9=0

We add all the numbers together, and all the variables

4.9H^2-26.5H-8.9=0

a = 4.9; b = -26.5; c = -8.9;
Δ = b2-4ac
Δ = -26.52-4·4.9·(-8.9)
Δ = 876.69
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{-(-26.5)-\sqrt{876.69}}{2*4.9}=\frac{26.5-\sqrt{876.69}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26.5)+\sqrt{876.69}}{2*4.9}=\frac{26.5+\sqrt{876.69}}{9.8}
$