6w^2+6w-7=0

Solution for 6w^2+6w-7=0 equation:

Simplifying
6w2 + 6w + -7 = 0

Reorder the terms:
-7 + 6w + 6w2 = 0

Solving
-7 + 6w + 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'.
-1.166666667 + w + w2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + w + 1.166666667 + w2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + w + w2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + w + w2 = 0 + 1.166666667
w + w2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
w + w2 = 1.166666667

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + w2 = 1.166666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + w2 = 1.166666667 + 0.25

Combine like terms: 1.166666667 + 0.25 = 1.416666667
1.25 + w2 = 1.416666667

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 1.416666667

Calculate the square root of the right side: 1.190238072

Break this problem into two subproblems by setting 
(w + 0.5) equal to 1.190238072 and -1.190238072.

Subproblem 1
w + 0.5 = 1.190238072

Simplifying
w + 0.5 = 1.190238072

Reorder the terms:
0.5 + w = 1.190238072

Solving
0.5 + w = 1.190238072

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 1.190238072 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 1.190238072 + -0.5
w = 1.190238072 + -0.5

Combine like terms: 1.190238072 + -0.5 = 0.690238072
w = 0.690238072

Simplifying
w = 0.690238072

Subproblem 2
w + 0.5 = -1.190238072

Simplifying
w + 0.5 = -1.190238072

Reorder the terms:
0.5 + w = -1.190238072

Solving
0.5 + w = -1.190238072

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -1.190238072 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -1.190238072 + -0.5
w = -1.190238072 + -0.5

Combine like terms: -1.190238072 + -0.5 = -1.690238072
w = -1.690238072

Simplifying
w = -1.690238072

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.690238072, -1.690238072}