20k^2-44k-39=0

Solution for 20k^2-44k-39=0 equation:

Simplifying
20k2 + -44k + -39 = 0

Reorder the terms:
-39 + -44k + 20k2 = 0

Solving
-39 + -44k + 20k2 = 0

Solving for variable 'k'.

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

Divide each side by '20'.
-1.95 + -2.2k + k2 = 0

Move the constant term to the right:

Add '1.95' to each side of the equation.
-1.95 + -2.2k + 1.95 + k2 = 0 + 1.95

Reorder the terms:
-1.95 + 1.95 + -2.2k + k2 = 0 + 1.95

Combine like terms: -1.95 + 1.95 = 0.00
0.00 + -2.2k + k2 = 0 + 1.95
-2.2k + k2 = 0 + 1.95

Combine like terms: 0 + 1.95 = 1.95
-2.2k + k2 = 1.95

The k term is -2.2k.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2k + 1.21 + k2 = 1.95 + 1.21

Reorder the terms:
1.21 + -2.2k + k2 = 1.95 + 1.21

Combine like terms: 1.95 + 1.21 = 3.16
1.21 + -2.2k + k2 = 3.16

Factor a perfect square on the left side:
(k + -1.1)(k + -1.1) = 3.16

Calculate the square root of the right side: 1.777638883

Break this problem into two subproblems by setting 
(k + -1.1) equal to 1.777638883 and -1.777638883.

Subproblem 1
k + -1.1 = 1.777638883

Simplifying
k + -1.1 = 1.777638883

Reorder the terms:
-1.1 + k = 1.777638883

Solving
-1.1 + k = 1.777638883

Solving for variable 'k'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + k = 1.777638883 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + k = 1.777638883 + 1.1
k = 1.777638883 + 1.1

Combine like terms: 1.777638883 + 1.1 = 2.877638883
k = 2.877638883

Simplifying
k = 2.877638883

Subproblem 2
k + -1.1 = -1.777638883

Simplifying
k + -1.1 = -1.777638883

Reorder the terms:
-1.1 + k = -1.777638883

Solving
-1.1 + k = -1.777638883

Solving for variable 'k'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + k = -1.777638883 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + k = -1.777638883 + 1.1
k = -1.777638883 + 1.1

Combine like terms: -1.777638883 + 1.1 = -0.677638883
k = -0.677638883

Simplifying
k = -0.677638883

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.877638883, -0.677638883}