12h^2+29h-15=0

Solution for 12h^2+29h-15=0 equation:

Simplifying
12h2 + 29h + -15 = 0

Reorder the terms:
-15 + 29h + 12h2 = 0

Solving
-15 + 29h + 12h2 = 0

Solving for variable 'h'.

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

Divide each side by '12'.
-1.25 + 2.416666667h + h2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 2.416666667h + 1.25 + h2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 2.416666667h + h2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 2.416666667h + h2 = 0 + 1.25
2.416666667h + h2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
2.416666667h + h2 = 1.25

The h term is 2.416666667h.  Take half its coefficient (1.208333334).
Square it (1.460069446) and add it to both sides.

Add '1.460069446' to each side of the equation.
2.416666667h + 1.460069446 + h2 = 1.25 + 1.460069446

Reorder the terms:
1.460069446 + 2.416666667h + h2 = 1.25 + 1.460069446

Combine like terms: 1.25 + 1.460069446 = 2.710069446
1.460069446 + 2.416666667h + h2 = 2.710069446

Factor a perfect square on the left side:
(h + 1.208333334)(h + 1.208333334) = 2.710069446

Calculate the square root of the right side: 1.646228856

Break this problem into two subproblems by setting 
(h + 1.208333334) equal to 1.646228856 and -1.646228856.

Subproblem 1
h + 1.208333334 = 1.646228856

Simplifying
h + 1.208333334 = 1.646228856

Reorder the terms:
1.208333334 + h = 1.646228856

Solving
1.208333334 + h = 1.646228856

Solving for variable 'h'.

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

Add '-1.208333334' to each side of the equation.
1.208333334 + -1.208333334 + h = 1.646228856 + -1.208333334

Combine like terms: 1.208333334 + -1.208333334 = 0.000000000
0.000000000 + h = 1.646228856 + -1.208333334
h = 1.646228856 + -1.208333334

Combine like terms: 1.646228856 + -1.208333334 = 0.437895522
h = 0.437895522

Simplifying
h = 0.437895522

Subproblem 2
h + 1.208333334 = -1.646228856

Simplifying
h + 1.208333334 = -1.646228856

Reorder the terms:
1.208333334 + h = -1.646228856

Solving
1.208333334 + h = -1.646228856

Solving for variable 'h'.

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

Add '-1.208333334' to each side of the equation.
1.208333334 + -1.208333334 + h = -1.646228856 + -1.208333334

Combine like terms: 1.208333334 + -1.208333334 = 0.000000000
0.000000000 + h = -1.646228856 + -1.208333334
h = -1.646228856 + -1.208333334

Combine like terms: -1.646228856 + -1.208333334 = -2.85456219
h = -2.85456219

Simplifying
h = -2.85456219

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {0.437895522, -2.85456219}