9b^2+15b-4=0

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Solution for 9b^2+15b-4=0 equation: 


Simplifying
9b2 + 15b + -4 = 0

Reorder the terms:
-4 + 15b + 9b2 = 0

Solving
-4 + 15b + 9b2 = 0

Solving for variable 'b'.

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

Divide each side by '9'.
-0.4444444444 + 1.666666667b + b2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + 1.666666667b + 0.4444444444 + b2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + 1.666666667b + b2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + 1.666666667b + b2 = 0 + 0.4444444444
1.666666667b + b2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
1.666666667b + b2 = 0.4444444444

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 = 0.4444444444 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667b + b2 = 0.4444444444 + 0.6944444447

Combine like terms: 0.4444444444 + 0.6944444447 = 1.1388888891
0.6944444447 + 1.666666667b + b2 = 1.1388888891

Factor a perfect square on the left side:
(b + 0.8333333335)(b + 0.8333333335) = 1.1388888891

Calculate the square root of the right side: 1.067187373

Break this problem into two subproblems by setting 
(b + 0.8333333335) equal to 1.067187373 and -1.067187373.


Subproblem 1
b + 0.8333333335 = 1.067187373

Simplifying
b + 0.8333333335 = 1.067187373

Reorder the terms:
0.8333333335 + b = 1.067187373

Solving
0.8333333335 + b = 1.067187373

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 = 1.067187373 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + b = 1.067187373 + -0.8333333335
b = 1.067187373 + -0.8333333335

Combine like terms: 1.067187373 + -0.8333333335 = 0.2338540395
b = 0.2338540395

Simplifying
b = 0.2338540395


Subproblem 2
b + 0.8333333335 = -1.067187373

Simplifying
b + 0.8333333335 = -1.067187373

Reorder the terms:
0.8333333335 + b = -1.067187373

Solving
0.8333333335 + b = -1.067187373

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 = -1.067187373 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + b = -1.067187373 + -0.8333333335
b = -1.067187373 + -0.8333333335

Combine like terms: -1.067187373 + -0.8333333335 = -1.9005207065
b = -1.9005207065

Simplifying
b = -1.9005207065


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.2338540395, -1.9005207065}

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