2x^2+4x-39=0

Solution for 2x^2+4x-39=0 equation:

Simplifying
2x2 + 4x + -39 = 0

Reorder the terms:
-39 + 4x + 2x2 = 0

Solving
-39 + 4x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-19.5 + 2x + x2 = 0

Move the constant term to the right:

Add '19.5' to each side of the equation.
-19.5 + 2x + 19.5 + x2 = 0 + 19.5

Reorder the terms:
-19.5 + 19.5 + 2x + x2 = 0 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + 2x + x2 = 0 + 19.5
2x + x2 = 0 + 19.5

Combine like terms: 0 + 19.5 = 19.5
2x + x2 = 19.5

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

Add '1' to each side of the equation.
2x + 1 + x2 = 19.5 + 1

Reorder the terms:
1 + 2x + x2 = 19.5 + 1

Combine like terms: 19.5 + 1 = 20.5
1 + 2x + x2 = 20.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 20.5

Calculate the square root of the right side: 4.527692569

Break this problem into two subproblems by setting 
(x + 1) equal to 4.527692569 and -4.527692569.

Subproblem 1
x + 1 = 4.527692569

Simplifying
x + 1 = 4.527692569

Reorder the terms:
1 + x = 4.527692569

Solving
1 + x = 4.527692569

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 4.527692569 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.527692569 + -1
x = 4.527692569 + -1

Combine like terms: 4.527692569 + -1 = 3.527692569
x = 3.527692569

Simplifying
x = 3.527692569

Subproblem 2
x + 1 = -4.527692569

Simplifying
x + 1 = -4.527692569

Reorder the terms:
1 + x = -4.527692569

Solving
1 + x = -4.527692569

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -4.527692569 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.527692569 + -1
x = -4.527692569 + -1

Combine like terms: -4.527692569 + -1 = -5.527692569
x = -5.527692569

Simplifying
x = -5.527692569

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.527692569, -5.527692569}