2w^2-4w=3

Solution for 2w^2-4w=3 equation:

Simplifying
2w2 + -4w = 3

Reorder the terms:
-4w + 2w2 = 3

Solving
-4w + 2w2 = 3

Solving for variable 'w'.

Reorder the terms:
-3 + -4w + 2w2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -4w + 2w2 = 0

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

Divide each side by '2'.
-1.5 + -2w + w2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -2w + 1.5 + w2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -2w + w2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -2w + w2 = 0 + 1.5
-2w + w2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-2w + w2 = 1.5

The w term is -2w.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2w + 1 + w2 = 1.5 + 1

Reorder the terms:
1 + -2w + w2 = 1.5 + 1

Combine like terms: 1.5 + 1 = 2.5
1 + -2w + w2 = 2.5

Factor a perfect square on the left side:
(w + -1)(w + -1) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(w + -1) equal to 1.58113883 and -1.58113883.

Subproblem 1
w + -1 = 1.58113883

Simplifying
w + -1 = 1.58113883

Reorder the terms:
-1 + w = 1.58113883

Solving
-1 + w = 1.58113883

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = 1.58113883 + 1

Combine like terms: -1 + 1 = 0
0 + w = 1.58113883 + 1
w = 1.58113883 + 1

Combine like terms: 1.58113883 + 1 = 2.58113883
w = 2.58113883

Simplifying
w = 2.58113883

Subproblem 2
w + -1 = -1.58113883

Simplifying
w + -1 = -1.58113883

Reorder the terms:
-1 + w = -1.58113883

Solving
-1 + w = -1.58113883

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = -1.58113883 + 1

Combine like terms: -1 + 1 = 0
0 + w = -1.58113883 + 1
w = -1.58113883 + 1

Combine like terms: -1.58113883 + 1 = -0.58113883
w = -0.58113883

Simplifying
w = -0.58113883

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.58113883, -0.58113883}