3w^2+4w-6=0

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Solution for 3w^2+4w-6=0 equation: 


Simplifying
3w2 + 4w + -6 = 0

Reorder the terms:
-6 + 4w + 3w2 = 0

Solving
-6 + 4w + 3w2 = 0

Solving for variable 'w'.

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

Divide each side by '3'.
-2 + 1.333333333w + w2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 1.333333333w + 2 + w2 = 0 + 2

Reorder the terms:
-2 + 2 + 1.333333333w + w2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 1.333333333w + w2 = 0 + 2
1.333333333w + w2 = 0 + 2

Combine like terms: 0 + 2 = 2
1.333333333w + w2 = 2

The w term is 1.333333333w.  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.
1.333333333w + 0.4444444442 + w2 = 2 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333w + w2 = 2 + 0.4444444442

Combine like terms: 2 + 0.4444444442 = 2.4444444442
0.4444444442 + 1.333333333w + w2 = 2.4444444442

Factor a perfect square on the left side:
(w + 0.6666666665)(w + 0.6666666665) = 2.4444444442

Calculate the square root of the right side: 1.56347192

Break this problem into two subproblems by setting 
(w + 0.6666666665) equal to 1.56347192 and -1.56347192.


Subproblem 1
w + 0.6666666665 = 1.56347192

Simplifying
w + 0.6666666665 = 1.56347192

Reorder the terms:
0.6666666665 + w = 1.56347192

Solving
0.6666666665 + w = 1.56347192

Solving for variable 'w'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + w = 1.56347192 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + w = 1.56347192 + -0.6666666665
w = 1.56347192 + -0.6666666665

Combine like terms: 1.56347192 + -0.6666666665 = 0.8968052535
w = 0.8968052535

Simplifying
w = 0.8968052535


Subproblem 2
w + 0.6666666665 = -1.56347192

Simplifying
w + 0.6666666665 = -1.56347192

Reorder the terms:
0.6666666665 + w = -1.56347192

Solving
0.6666666665 + w = -1.56347192

Solving for variable 'w'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + w = -1.56347192 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + w = -1.56347192 + -0.6666666665
w = -1.56347192 + -0.6666666665

Combine like terms: -1.56347192 + -0.6666666665 = -2.2301385865
w = -2.2301385865

Simplifying
w = -2.2301385865


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.8968052535, -2.2301385865}

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