3b^2-4b-72=0

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Solution for 3b^2-4b-72=0 equation: 


Simplifying
3b2 + -4b + -72 = 0

Reorder the terms:
-72 + -4b + 3b2 = 0

Solving
-72 + -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'.
-24 + -1.333333333b + b2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -1.333333333b + 24 + b2 = 0 + 24

Reorder the terms:
-24 + 24 + -1.333333333b + b2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1.333333333b + b2 = 0 + 24
-1.333333333b + b2 = 0 + 24

Combine like terms: 0 + 24 = 24
-1.333333333b + b2 = 24

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 = 24 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333b + b2 = 24 + 0.4444444442

Combine like terms: 24 + 0.4444444442 = 24.4444444442
0.4444444442 + -1.333333333b + b2 = 24.4444444442

Factor a perfect square on the left side:
(b + -0.6666666665)(b + -0.6666666665) = 24.4444444442

Calculate the square root of the right side: 4.944132325

Break this problem into two subproblems by setting 
(b + -0.6666666665) equal to 4.944132325 and -4.944132325.


Subproblem 1
b + -0.6666666665 = 4.944132325

Simplifying
b + -0.6666666665 = 4.944132325

Reorder the terms:
-0.6666666665 + b = 4.944132325

Solving
-0.6666666665 + b = 4.944132325

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 = 4.944132325 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + b = 4.944132325 + 0.6666666665
b = 4.944132325 + 0.6666666665

Combine like terms: 4.944132325 + 0.6666666665 = 5.6107989915
b = 5.6107989915

Simplifying
b = 5.6107989915


Subproblem 2
b + -0.6666666665 = -4.944132325

Simplifying
b + -0.6666666665 = -4.944132325

Reorder the terms:
-0.6666666665 + b = -4.944132325

Solving
-0.6666666665 + b = -4.944132325

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 = -4.944132325 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + b = -4.944132325 + 0.6666666665
b = -4.944132325 + 0.6666666665

Combine like terms: -4.944132325 + 0.6666666665 = -4.2774656585
b = -4.2774656585

Simplifying
b = -4.2774656585


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {5.6107989915, -4.2774656585}

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