6k^2-43k-20=0

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Solution for 6k^2-43k-20=0 equation: 


Simplifying
6k2 + -43k + -20 = 0

Reorder the terms:
-20 + -43k + 6k2 = 0

Solving
-20 + -43k + 6k2 = 0

Solving for variable 'k'.

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

Divide each side by '6'.
-3.333333333 + -7.166666667k + k2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -7.166666667k + 3.333333333 + k2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -7.166666667k + k2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -7.166666667k + k2 = 0 + 3.333333333
-7.166666667k + k2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-7.166666667k + k2 = 3.333333333

The k term is -7.166666667k.  Take half its coefficient (-3.583333334).
Square it (12.84027778) and add it to both sides.

Add '12.84027778' to each side of the equation.
-7.166666667k + 12.84027778 + k2 = 3.333333333 + 12.84027778

Reorder the terms:
12.84027778 + -7.166666667k + k2 = 3.333333333 + 12.84027778

Combine like terms: 3.333333333 + 12.84027778 = 16.173611113
12.84027778 + -7.166666667k + k2 = 16.173611113

Factor a perfect square on the left side:
(k + -3.583333334)(k + -3.583333334) = 16.173611113

Calculate the square root of the right side: 4.021642838

Break this problem into two subproblems by setting 
(k + -3.583333334) equal to 4.021642838 and -4.021642838.


Subproblem 1
k + -3.583333334 = 4.021642838

Simplifying
k + -3.583333334 = 4.021642838

Reorder the terms:
-3.583333334 + k = 4.021642838

Solving
-3.583333334 + k = 4.021642838

Solving for variable 'k'.

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

Add '3.583333334' to each side of the equation.
-3.583333334 + 3.583333334 + k = 4.021642838 + 3.583333334

Combine like terms: -3.583333334 + 3.583333334 = 0.000000000
0.000000000 + k = 4.021642838 + 3.583333334
k = 4.021642838 + 3.583333334

Combine like terms: 4.021642838 + 3.583333334 = 7.604976172
k = 7.604976172

Simplifying
k = 7.604976172


Subproblem 2
k + -3.583333334 = -4.021642838

Simplifying
k + -3.583333334 = -4.021642838

Reorder the terms:
-3.583333334 + k = -4.021642838

Solving
-3.583333334 + k = -4.021642838

Solving for variable 'k'.

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

Add '3.583333334' to each side of the equation.
-3.583333334 + 3.583333334 + k = -4.021642838 + 3.583333334

Combine like terms: -3.583333334 + 3.583333334 = 0.000000000
0.000000000 + k = -4.021642838 + 3.583333334
k = -4.021642838 + 3.583333334

Combine like terms: -4.021642838 + 3.583333334 = -0.438309504
k = -0.438309504

Simplifying
k = -0.438309504


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {7.604976172, -0.438309504}

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