27x^2-6+59x=0

Solution for 27x^2-6+59x=0 equation:

Simplifying
27x2 + -6 + 59x = 0

Reorder the terms:
-6 + 59x + 27x2 = 0

Solving
-6 + 59x + 27x2 = 0

Solving for variable 'x'.

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

Divide each side by '27'.
-0.2222222222 + 2.185185185x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 2.185185185x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + 2.185185185x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + 2.185185185x + x2 = 0 + 0.2222222222
2.185185185x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
2.185185185x + x2 = 0.2222222222

The x term is 2.185185185x.  Take half its coefficient (1.092592593).
Square it (1.193758574) and add it to both sides.

Add '1.193758574' to each side of the equation.
2.185185185x + 1.193758574 + x2 = 0.2222222222 + 1.193758574

Reorder the terms:
1.193758574 + 2.185185185x + x2 = 0.2222222222 + 1.193758574

Combine like terms: 0.2222222222 + 1.193758574 = 1.4159807962
1.193758574 + 2.185185185x + x2 = 1.4159807962

Factor a perfect square on the left side:
(x + 1.092592593)(x + 1.092592593) = 1.4159807962

Calculate the square root of the right side: 1.189949913

Break this problem into two subproblems by setting 
(x + 1.092592593) equal to 1.189949913 and -1.189949913.

Subproblem 1
x + 1.092592593 = 1.189949913

Simplifying
x + 1.092592593 = 1.189949913

Reorder the terms:
1.092592593 + x = 1.189949913

Solving
1.092592593 + x = 1.189949913

Solving for variable 'x'.

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

Add '-1.092592593' to each side of the equation.
1.092592593 + -1.092592593 + x = 1.189949913 + -1.092592593

Combine like terms: 1.092592593 + -1.092592593 = 0.000000000
0.000000000 + x = 1.189949913 + -1.092592593
x = 1.189949913 + -1.092592593

Combine like terms: 1.189949913 + -1.092592593 = 0.09735732
x = 0.09735732

Simplifying
x = 0.09735732

Subproblem 2
x + 1.092592593 = -1.189949913

Simplifying
x + 1.092592593 = -1.189949913

Reorder the terms:
1.092592593 + x = -1.189949913

Solving
1.092592593 + x = -1.189949913

Solving for variable 'x'.

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

Add '-1.092592593' to each side of the equation.
1.092592593 + -1.092592593 + x = -1.189949913 + -1.092592593

Combine like terms: 1.092592593 + -1.092592593 = 0.000000000
0.000000000 + x = -1.189949913 + -1.092592593
x = -1.189949913 + -1.092592593

Combine like terms: -1.189949913 + -1.092592593 = -2.282542506
x = -2.282542506

Simplifying
x = -2.282542506

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.09735732, -2.282542506}