7w^2-4w-6=0

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Solution for 7w^2-4w-6=0 equation: 


Simplifying
7w2 + -4w + -6 = 0

Reorder the terms:
-6 + -4w + 7w2 = 0

Solving
-6 + -4w + 7w2 = 0

Solving for variable 'w'.

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

Divide each side by '7'.
-0.8571428571 + -0.5714285714w + w2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + -0.5714285714w + 0.8571428571 + w2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + -0.5714285714w + w2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + -0.5714285714w + w2 = 0 + 0.8571428571
-0.5714285714w + w2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
-0.5714285714w + w2 = 0.8571428571

The w term is -0.5714285714w.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714w + 0.08163265305 + w2 = 0.8571428571 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714w + w2 = 0.8571428571 + 0.08163265305

Combine like terms: 0.8571428571 + 0.08163265305 = 0.93877551015
0.08163265305 + -0.5714285714w + w2 = 0.93877551015

Factor a perfect square on the left side:
(w + -0.2857142857)(w + -0.2857142857) = 0.93877551015

Calculate the square root of the right side: 0.968904283

Break this problem into two subproblems by setting 
(w + -0.2857142857) equal to 0.968904283 and -0.968904283.


Subproblem 1
w + -0.2857142857 = 0.968904283

Simplifying
w + -0.2857142857 = 0.968904283

Reorder the terms:
-0.2857142857 + w = 0.968904283

Solving
-0.2857142857 + w = 0.968904283

Solving for variable 'w'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + w = 0.968904283 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + w = 0.968904283 + 0.2857142857
w = 0.968904283 + 0.2857142857

Combine like terms: 0.968904283 + 0.2857142857 = 1.2546185687
w = 1.2546185687

Simplifying
w = 1.2546185687


Subproblem 2
w + -0.2857142857 = -0.968904283

Simplifying
w + -0.2857142857 = -0.968904283

Reorder the terms:
-0.2857142857 + w = -0.968904283

Solving
-0.2857142857 + w = -0.968904283

Solving for variable 'w'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + w = -0.968904283 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + w = -0.968904283 + 0.2857142857
w = -0.968904283 + 0.2857142857

Combine like terms: -0.968904283 + 0.2857142857 = -0.6831899973
w = -0.6831899973

Simplifying
w = -0.6831899973


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.2546185687, -0.6831899973}

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