3b^2+5b-82=0

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Solution for 3b^2+5b-82=0 equation: 


Simplifying
3b2 + 5b + -82 = 0

Reorder the terms:
-82 + 5b + 3b2 = 0

Solving
-82 + 5b + 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'.
-27.33333333 + 1.666666667b + b2 = 0

Move the constant term to the right:

Add '27.33333333' to each side of the equation.
-27.33333333 + 1.666666667b + 27.33333333 + b2 = 0 + 27.33333333

Reorder the terms:
-27.33333333 + 27.33333333 + 1.666666667b + b2 = 0 + 27.33333333

Combine like terms: -27.33333333 + 27.33333333 = 0.00000000
0.00000000 + 1.666666667b + b2 = 0 + 27.33333333
1.666666667b + b2 = 0 + 27.33333333

Combine like terms: 0 + 27.33333333 = 27.33333333
1.666666667b + b2 = 27.33333333

The b term is 1.666666667b.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667b + 0.6944444447 + b2 = 27.33333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667b + b2 = 27.33333333 + 0.6944444447

Combine like terms: 27.33333333 + 0.6944444447 = 28.0277777747
0.6944444447 + 1.666666667b + b2 = 28.0277777747

Factor a perfect square on the left side:
(b + 0.8333333335)(b + 0.8333333335) = 28.0277777747

Calculate the square root of the right side: 5.294126724

Break this problem into two subproblems by setting 
(b + 0.8333333335) equal to 5.294126724 and -5.294126724.


Subproblem 1
b + 0.8333333335 = 5.294126724

Simplifying
b + 0.8333333335 = 5.294126724

Reorder the terms:
0.8333333335 + b = 5.294126724

Solving
0.8333333335 + b = 5.294126724

Solving for variable 'b'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + b = 5.294126724 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + b = 5.294126724 + -0.8333333335
b = 5.294126724 + -0.8333333335

Combine like terms: 5.294126724 + -0.8333333335 = 4.4607933905
b = 4.4607933905

Simplifying
b = 4.4607933905


Subproblem 2
b + 0.8333333335 = -5.294126724

Simplifying
b + 0.8333333335 = -5.294126724

Reorder the terms:
0.8333333335 + b = -5.294126724

Solving
0.8333333335 + b = -5.294126724

Solving for variable 'b'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + b = -5.294126724 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + b = -5.294126724 + -0.8333333335
b = -5.294126724 + -0.8333333335

Combine like terms: -5.294126724 + -0.8333333335 = -6.1274600575
b = -6.1274600575

Simplifying
b = -6.1274600575


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4.4607933905, -6.1274600575}

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