H=-4.9t^2-14.7t+19.6

Solution for H=-4.9t^2-14.7t+19.6 equation:

=-4.9H^2-14.7H+19.6

We move all terms to the left:

-(-4.9H^2-14.7H+19.6)=0

We get rid of parentheses

4.9H^2+14.7H-19.6=0

a = 4.9; b = 14.7; c = -19.6;
Δ = b2-4ac
Δ = 14.72-4·4.9·(-19.6)
Δ = 600.25
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{-(14.7)-\sqrt{600.25}}{2*4.9}=\frac{-14.7-\sqrt{600.25}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14.7)+\sqrt{600.25}}{2*4.9}=\frac{-14.7+\sqrt{600.25}}{9.8}
$