7k^2+9k-5=0

Solution for 7k^2+9k-5=0 equation:

Simplifying
7k2 + 9k + -5 = 0

Reorder the terms:
-5 + 9k + 7k2 = 0

Solving
-5 + 9k + 7k2 = 0

Solving for variable 'k'.

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

Divide each side by '7'.
-0.7142857143 + 1.285714286k + k2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 1.285714286k + 0.7142857143 + k2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 1.285714286k + k2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 1.285714286k + k2 = 0 + 0.7142857143
1.285714286k + k2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
1.285714286k + k2 = 0.7142857143

The k term is 1.285714286k.  Take half its coefficient (0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
1.285714286k + 0.4132653063 + k2 = 0.7142857143 + 0.4132653063

Reorder the terms:
0.4132653063 + 1.285714286k + k2 = 0.7142857143 + 0.4132653063

Combine like terms: 0.7142857143 + 0.4132653063 = 1.1275510206
0.4132653063 + 1.285714286k + k2 = 1.1275510206

Factor a perfect square on the left side:
(k + 0.642857143)(k + 0.642857143) = 1.1275510206

Calculate the square root of the right side: 1.061862053

Break this problem into two subproblems by setting 
(k + 0.642857143) equal to 1.061862053 and -1.061862053.

Subproblem 1
k + 0.642857143 = 1.061862053

Simplifying
k + 0.642857143 = 1.061862053

Reorder the terms:
0.642857143 + k = 1.061862053

Solving
0.642857143 + k = 1.061862053

Solving for variable 'k'.

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

Add '-0.642857143' to each side of the equation.
0.642857143 + -0.642857143 + k = 1.061862053 + -0.642857143

Combine like terms: 0.642857143 + -0.642857143 = 0.000000000
0.000000000 + k = 1.061862053 + -0.642857143
k = 1.061862053 + -0.642857143

Combine like terms: 1.061862053 + -0.642857143 = 0.41900491
k = 0.41900491

Simplifying
k = 0.41900491

Subproblem 2
k + 0.642857143 = -1.061862053

Simplifying
k + 0.642857143 = -1.061862053

Reorder the terms:
0.642857143 + k = -1.061862053

Solving
0.642857143 + k = -1.061862053

Solving for variable 'k'.

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

Add '-0.642857143' to each side of the equation.
0.642857143 + -0.642857143 + k = -1.061862053 + -0.642857143

Combine like terms: 0.642857143 + -0.642857143 = 0.000000000
0.000000000 + k = -1.061862053 + -0.642857143
k = -1.061862053 + -0.642857143

Combine like terms: -1.061862053 + -0.642857143 = -1.704719196
k = -1.704719196

Simplifying
k = -1.704719196

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.41900491, -1.704719196}