9k^2-5k-3=0

Solution for 9k^2-5k-3=0 equation:

Simplifying
9k2 + -5k + -3 = 0

Reorder the terms:
-3 + -5k + 9k2 = 0

Solving
-3 + -5k + 9k2 = 0

Solving for variable 'k'.

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

Divide each side by '9'.
-0.3333333333 + -0.5555555556k + k2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -0.5555555556k + 0.3333333333 + k2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -0.5555555556k + k2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -0.5555555556k + k2 = 0 + 0.3333333333
-0.5555555556k + k2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-0.5555555556k + k2 = 0.3333333333

The k term is -0.5555555556k.  Take half its coefficient (-0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
-0.5555555556k + 0.07716049384 + k2 = 0.3333333333 + 0.07716049384

Reorder the terms:
0.07716049384 + -0.5555555556k + k2 = 0.3333333333 + 0.07716049384

Combine like terms: 0.3333333333 + 0.07716049384 = 0.41049382714
0.07716049384 + -0.5555555556k + k2 = 0.41049382714

Factor a perfect square on the left side:
(k + -0.2777777778)(k + -0.2777777778) = 0.41049382714

Calculate the square root of the right side: 0.640697922

Break this problem into two subproblems by setting 
(k + -0.2777777778) equal to 0.640697922 and -0.640697922.

Subproblem 1
k + -0.2777777778 = 0.640697922

Simplifying
k + -0.2777777778 = 0.640697922

Reorder the terms:
-0.2777777778 + k = 0.640697922

Solving
-0.2777777778 + k = 0.640697922

Solving for variable 'k'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + k = 0.640697922 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + k = 0.640697922 + 0.2777777778
k = 0.640697922 + 0.2777777778

Combine like terms: 0.640697922 + 0.2777777778 = 0.9184756998
k = 0.9184756998

Simplifying
k = 0.9184756998

Subproblem 2
k + -0.2777777778 = -0.640697922

Simplifying
k + -0.2777777778 = -0.640697922

Reorder the terms:
-0.2777777778 + k = -0.640697922

Solving
-0.2777777778 + k = -0.640697922

Solving for variable 'k'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + k = -0.640697922 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + k = -0.640697922 + 0.2777777778
k = -0.640697922 + 0.2777777778

Combine like terms: -0.640697922 + 0.2777777778 = -0.3629201442
k = -0.3629201442

Simplifying
k = -0.3629201442

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.9184756998, -0.3629201442}