8x^2+20x-13=0

Solution for 8x^2+20x-13=0 equation:

Simplifying
8x2 + 20x + -13 = 0

Reorder the terms:
-13 + 20x + 8x2 = 0

Solving
-13 + 20x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-1.625 + 2.5x + x2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + 2.5x + 1.625 + x2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + 2.5x + x2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + 2.5x + x2 = 0 + 1.625
2.5x + x2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
2.5x + x2 = 1.625

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 1.625 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 1.625 + 1.5625

Combine like terms: 1.625 + 1.5625 = 3.1875
1.5625 + 2.5x + x2 = 3.1875

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 3.1875

Calculate the square root of the right side: 1.785357107

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.785357107 and -1.785357107.

Subproblem 1
x + 1.25 = 1.785357107

Simplifying
x + 1.25 = 1.785357107

Reorder the terms:
1.25 + x = 1.785357107

Solving
1.25 + x = 1.785357107

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 1.785357107 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 1.785357107 + -1.25
x = 1.785357107 + -1.25

Combine like terms: 1.785357107 + -1.25 = 0.535357107
x = 0.535357107

Simplifying
x = 0.535357107

Subproblem 2
x + 1.25 = -1.785357107

Simplifying
x + 1.25 = -1.785357107

Reorder the terms:
1.25 + x = -1.785357107

Solving
1.25 + x = -1.785357107

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -1.785357107 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -1.785357107 + -1.25
x = -1.785357107 + -1.25

Combine like terms: -1.785357107 + -1.25 = -3.035357107
x = -3.035357107

Simplifying
x = -3.035357107

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.535357107, -3.035357107}