3h^2+4h-1224=0

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Solution for 3h^2+4h-1224=0 equation:


Simplifying
3h2 + 4h + -1224 = 0

Reorder the terms:
-1224 + 4h + 3h2 = 0

Solving
-1224 + 4h + 3h2 = 0

Solving for variable 'h'.

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

Divide each side by '3'.
-408 + 1.333333333h + h2 = 0

Move the constant term to the right:

Add '408' to each side of the equation.
-408 + 1.333333333h + 408 + h2 = 0 + 408

Reorder the terms:
-408 + 408 + 1.333333333h + h2 = 0 + 408

Combine like terms: -408 + 408 = 0
0 + 1.333333333h + h2 = 0 + 408
1.333333333h + h2 = 0 + 408

Combine like terms: 0 + 408 = 408
1.333333333h + h2 = 408

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 = 408 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333h + h2 = 408 + 0.4444444442

Combine like terms: 408 + 0.4444444442 = 408.4444444442
0.4444444442 + 1.333333333h + h2 = 408.4444444442

Factor a perfect square on the left side:
(h + 0.6666666665)(h + 0.6666666665) = 408.4444444442

Calculate the square root of the right side: 20.210008522

Break this problem into two subproblems by setting 
(h + 0.6666666665) equal to 20.210008522 and -20.210008522.

Subproblem 1

h + 0.6666666665 = 20.210008522 Simplifying h + 0.6666666665 = 20.210008522 Reorder the terms: 0.6666666665 + h = 20.210008522 Solving 0.6666666665 + h = 20.210008522 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 = 20.210008522 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + h = 20.210008522 + -0.6666666665 h = 20.210008522 + -0.6666666665 Combine like terms: 20.210008522 + -0.6666666665 = 19.5433418555 h = 19.5433418555 Simplifying h = 19.5433418555

Subproblem 2

h + 0.6666666665 = -20.210008522 Simplifying h + 0.6666666665 = -20.210008522 Reorder the terms: 0.6666666665 + h = -20.210008522 Solving 0.6666666665 + h = -20.210008522 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 = -20.210008522 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + h = -20.210008522 + -0.6666666665 h = -20.210008522 + -0.6666666665 Combine like terms: -20.210008522 + -0.6666666665 = -20.8766751885 h = -20.8766751885 Simplifying h = -20.8766751885

Solution

The solution to the problem is based on the solutions from the subproblems. h = {19.5433418555, -20.8766751885}

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