3b^2-4b-126=0

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Solution for 3b^2-4b-126=0 equation: 


Simplifying
3b2 + -4b + -126 = 0

Reorder the terms:
-126 + -4b + 3b2 = 0

Solving
-126 + -4b + 3b2 = 0

Solving for variable 'b'.

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

Divide each side by '3'.
-42 + -1.333333333b + b2 = 0

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + -1.333333333b + 42 + b2 = 0 + 42

Reorder the terms:
-42 + 42 + -1.333333333b + b2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -1.333333333b + b2 = 0 + 42
-1.333333333b + b2 = 0 + 42

Combine like terms: 0 + 42 = 42
-1.333333333b + b2 = 42

The b term is -1.333333333b.  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.
-1.333333333b + 0.4444444442 + b2 = 42 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333b + b2 = 42 + 0.4444444442

Combine like terms: 42 + 0.4444444442 = 42.4444444442
0.4444444442 + -1.333333333b + b2 = 42.4444444442

Factor a perfect square on the left side:
(b + -0.6666666665)(b + -0.6666666665) = 42.4444444442

Calculate the square root of the right side: 6.514940095

Break this problem into two subproblems by setting 
(b + -0.6666666665) equal to 6.514940095 and -6.514940095.


Subproblem 1
b + -0.6666666665 = 6.514940095

Simplifying
b + -0.6666666665 = 6.514940095

Reorder the terms:
-0.6666666665 + b = 6.514940095

Solving
-0.6666666665 + b = 6.514940095

Solving for variable 'b'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + b = 6.514940095 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + b = 6.514940095 + 0.6666666665
b = 6.514940095 + 0.6666666665

Combine like terms: 6.514940095 + 0.6666666665 = 7.1816067615
b = 7.1816067615

Simplifying
b = 7.1816067615


Subproblem 2
b + -0.6666666665 = -6.514940095

Simplifying
b + -0.6666666665 = -6.514940095

Reorder the terms:
-0.6666666665 + b = -6.514940095

Solving
-0.6666666665 + b = -6.514940095

Solving for variable 'b'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + b = -6.514940095 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + b = -6.514940095 + 0.6666666665
b = -6.514940095 + 0.6666666665

Combine like terms: -6.514940095 + 0.6666666665 = -5.8482734285
b = -5.8482734285

Simplifying
b = -5.8482734285


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {7.1816067615, -5.8482734285}

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