5k^2+6k-1=0

Solution for 5k^2+6k-1=0 equation:

Simplifying
5k2 + 6k + -1 = 0

Reorder the terms:
-1 + 6k + 5k2 = 0

Solving
-1 + 6k + 5k2 = 0

Solving for variable 'k'.

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

Divide each side by '5'.
-0.2 + 1.2k + k2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 1.2k + 0.2 + k2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 1.2k + k2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 1.2k + k2 = 0 + 0.2
1.2k + k2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
1.2k + k2 = 0.2

The k term is 1.2k.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2k + 0.36 + k2 = 0.2 + 0.36

Reorder the terms:
0.36 + 1.2k + k2 = 0.2 + 0.36

Combine like terms: 0.2 + 0.36 = 0.56
0.36 + 1.2k + k2 = 0.56

Factor a perfect square on the left side:
(k + 0.6)(k + 0.6) = 0.56

Calculate the square root of the right side: 0.748331477

Break this problem into two subproblems by setting 
(k + 0.6) equal to 0.748331477 and -0.748331477.

Subproblem 1
k + 0.6 = 0.748331477

Simplifying
k + 0.6 = 0.748331477

Reorder the terms:
0.6 + k = 0.748331477

Solving
0.6 + k = 0.748331477

Solving for variable 'k'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + k = 0.748331477 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + k = 0.748331477 + -0.6
k = 0.748331477 + -0.6

Combine like terms: 0.748331477 + -0.6 = 0.148331477
k = 0.148331477

Simplifying
k = 0.148331477

Subproblem 2
k + 0.6 = -0.748331477

Simplifying
k + 0.6 = -0.748331477

Reorder the terms:
0.6 + k = -0.748331477

Solving
0.6 + k = -0.748331477

Solving for variable 'k'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + k = -0.748331477 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + k = -0.748331477 + -0.6
k = -0.748331477 + -0.6

Combine like terms: -0.748331477 + -0.6 = -1.348331477
k = -1.348331477

Simplifying
k = -1.348331477

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.148331477, -1.348331477}