2k^2+4k=3

Solution for 2k^2+4k=3 equation:

Simplifying
2k2 + 4k = 3

Reorder the terms:
4k + 2k2 = 3

Solving
4k + 2k2 = 3

Solving for variable 'k'.

Reorder the terms:
-3 + 4k + 2k2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 4k + 2k2 = 0

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

Divide each side by '2'.
-1.5 + 2k + k2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 2k + 1.5 + k2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 2k + k2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 2k + k2 = 0 + 1.5
2k + k2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
2k + k2 = 1.5

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

Add '1' to each side of the equation.
2k + 1 + k2 = 1.5 + 1

Reorder the terms:
1 + 2k + k2 = 1.5 + 1

Combine like terms: 1.5 + 1 = 2.5
1 + 2k + k2 = 2.5

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

Calculate the square root of the right side: 1.58113883

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

Subproblem 1
k + 1 = 1.58113883

Simplifying
k + 1 = 1.58113883

Reorder the terms:
1 + k = 1.58113883

Solving
1 + k = 1.58113883

Solving for variable 'k'.

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

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

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

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

Simplifying
k = 0.58113883

Subproblem 2
k + 1 = -1.58113883

Simplifying
k + 1 = -1.58113883

Reorder the terms:
1 + k = -1.58113883

Solving
1 + k = -1.58113883

Solving for variable 'k'.

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

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

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

Combine like terms: -1.58113883 + -1 = -2.58113883
k = -2.58113883

Simplifying
k = -2.58113883

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