0.4h^2+0.8h=0.2

Solution for 0.4h^2+0.8h=0.2 equation:

Simplifying
0.4h2 + 0.8h = 0.2

Reorder the terms:
0.8h + 0.4h2 = 0.2

Solving
0.8h + 0.4h2 = 0.2

Solving for variable 'h'.

Reorder the terms:
-0.2 + 0.8h + 0.4h2 = 0.2 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
-0.2 + 0.8h + 0.4h2 = 0.0

Begin completing the square.  Divide all terms by
0.4 the coefficient of the squared term: 

Divide each side by '0.4'.
-0.5 + 2h + h2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2h + 0.5 + h2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2h + h2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2h + h2 = 0 + 0.5
2h + h2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2h + h2 = 0.5

The h term is 2h.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2h + 1 + h2 = 0.5 + 1

Reorder the terms:
1 + 2h + h2 = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
1 + 2h + h2 = 1.5

Factor a perfect square on the left side:
(h + 1)(h + 1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(h + 1) equal to 1.224744871 and -1.224744871.

Subproblem 1
h + 1 = 1.224744871

Simplifying
h + 1 = 1.224744871

Reorder the terms:
1 + h = 1.224744871

Solving
1 + h = 1.224744871

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + h = 1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + h = 1.224744871 + -1
h = 1.224744871 + -1

Combine like terms: 1.224744871 + -1 = 0.224744871
h = 0.224744871

Simplifying
h = 0.224744871

Subproblem 2
h + 1 = -1.224744871

Simplifying
h + 1 = -1.224744871

Reorder the terms:
1 + h = -1.224744871

Solving
1 + h = -1.224744871

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + h = -1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + h = -1.224744871 + -1
h = -1.224744871 + -1

Combine like terms: -1.224744871 + -1 = -2.224744871
h = -2.224744871

Simplifying
h = -2.224744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {0.224744871, -2.224744871}