6w^2+4w-9=0

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Solution for 6w^2+4w-9=0 equation: 


Simplifying
6w2 + 4w + -9 = 0

Reorder the terms:
-9 + 4w + 6w2 = 0

Solving
-9 + 4w + 6w2 = 0

Solving for variable 'w'.

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

Divide each side by '6'.
-1.5 + 0.6666666667w + w2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.6666666667w + 1.5 + w2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.6666666667w + w2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.6666666667w + w2 = 0 + 1.5
0.6666666667w + w2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
0.6666666667w + w2 = 1.5

The w term is 0.6666666667w.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667w + 0.1111111112 + w2 = 1.5 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667w + w2 = 1.5 + 0.1111111112

Combine like terms: 1.5 + 0.1111111112 = 1.6111111112
0.1111111112 + 0.6666666667w + w2 = 1.6111111112

Factor a perfect square on the left side:
(w + 0.3333333334)(w + 0.3333333334) = 1.6111111112

Calculate the square root of the right side: 1.269295518

Break this problem into two subproblems by setting 
(w + 0.3333333334) equal to 1.269295518 and -1.269295518.


Subproblem 1
w + 0.3333333334 = 1.269295518

Simplifying
w + 0.3333333334 = 1.269295518

Reorder the terms:
0.3333333334 + w = 1.269295518

Solving
0.3333333334 + w = 1.269295518

Solving for variable 'w'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + w = 1.269295518 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + w = 1.269295518 + -0.3333333334
w = 1.269295518 + -0.3333333334

Combine like terms: 1.269295518 + -0.3333333334 = 0.9359621846
w = 0.9359621846

Simplifying
w = 0.9359621846


Subproblem 2
w + 0.3333333334 = -1.269295518

Simplifying
w + 0.3333333334 = -1.269295518

Reorder the terms:
0.3333333334 + w = -1.269295518

Solving
0.3333333334 + w = -1.269295518

Solving for variable 'w'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + w = -1.269295518 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + w = -1.269295518 + -0.3333333334
w = -1.269295518 + -0.3333333334

Combine like terms: -1.269295518 + -0.3333333334 = -1.6026288514
w = -1.6026288514

Simplifying
w = -1.6026288514


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.9359621846, -1.6026288514}

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