9h^2-12h-4=4

Solution for 9h^2-12h-4=4 equation:

Simplifying
9h2 + -12h + -4 = 4

Reorder the terms:
-4 + -12h + 9h2 = 4

Solving
-4 + -12h + 9h2 = 4

Solving for variable 'h'.

Reorder the terms:
-4 + -4 + -12h + 9h2 = 4 + -4

Combine like terms: -4 + -4 = -8
-8 + -12h + 9h2 = 4 + -4

Combine like terms: 4 + -4 = 0
-8 + -12h + 9h2 = 0

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

Divide each side by '9'.
-0.8888888889 + -1.333333333h + h2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + -1.333333333h + 0.8888888889 + h2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + -1.333333333h + h2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + -1.333333333h + h2 = 0 + 0.8888888889
-1.333333333h + h2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
-1.333333333h + h2 = 0.8888888889

The h term is -1.333333333h.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333h + 0.4444444442 + h2 = 0.8888888889 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333h + h2 = 0.8888888889 + 0.4444444442

Combine like terms: 0.8888888889 + 0.4444444442 = 1.3333333331
0.4444444442 + -1.333333333h + h2 = 1.3333333331

Factor a perfect square on the left side:
(h + -0.6666666665)(h + -0.6666666665) = 1.3333333331

Calculate the square root of the right side: 1.154700538

Break this problem into two subproblems by setting 
(h + -0.6666666665) equal to 1.154700538 and -1.154700538.

Subproblem 1
h + -0.6666666665 = 1.154700538

Simplifying
h + -0.6666666665 = 1.154700538

Reorder the terms:
-0.6666666665 + h = 1.154700538

Solving
-0.6666666665 + h = 1.154700538

Solving for variable 'h'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + h = 1.154700538 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + h = 1.154700538 + 0.6666666665
h = 1.154700538 + 0.6666666665

Combine like terms: 1.154700538 + 0.6666666665 = 1.8213672045
h = 1.8213672045

Simplifying
h = 1.8213672045

Subproblem 2
h + -0.6666666665 = -1.154700538

Simplifying
h + -0.6666666665 = -1.154700538

Reorder the terms:
-0.6666666665 + h = -1.154700538

Solving
-0.6666666665 + h = -1.154700538

Solving for variable 'h'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + h = -1.154700538 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + h = -1.154700538 + 0.6666666665
h = -1.154700538 + 0.6666666665

Combine like terms: -1.154700538 + 0.6666666665 = -0.4880338715
h = -0.4880338715

Simplifying
h = -0.4880338715

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {1.8213672045, -0.4880338715}