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 = 0.58113883
W = 0.58113883

Simplifying
W = 0.58113883

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 = -2.58113883
W = -2.58113883

Simplifying
W = -2.58113883

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