H=-4.9t^2+19.6+0.4

Solution for H=-4.9t^2+19.6+0.4 equation:

=-4.9H^2+19.6+0.4

We move all terms to the left:

-(-4.9H^2+19.6+0.4)=0

We get rid of parentheses

4.9H^2-19.6-0.4=0

We add all the numbers together, and all the variables

4.9H^2-20=0

a = 4.9; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·4.9·(-20)
Δ = 392
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{2}}{2*4.9}=\frac{0-14\sqrt{2}}{9.8}
=-\frac{14\sqrt{2}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{2}}{2*4.9}=\frac{0+14\sqrt{2}}{9.8}
=\frac{14\sqrt{2}}{9.8}
$