60x^2-130x+6=0

Solution for 60x^2-130x+6=0 equation:

Simplifying
60x2 + -130x + 6 = 0

Reorder the terms:
6 + -130x + 60x2 = 0

Solving
6 + -130x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -65x + 30x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -65x + 30x2)' equal to zero and attempt to solve:

Simplifying
3 + -65x + 30x2 = 0

Solving
3 + -65x + 30x2 = 0

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

Divide each side by '30'.
0.1 + -2.166666667x + x2 = 0.0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -2.166666667x + -0.1 + x2 = 0.0 + -0.1

Reorder the terms:
0.1 + -0.1 + -2.166666667x + x2 = 0.0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -2.166666667x + x2 = 0.0 + -0.1
-2.166666667x + x2 = 0.0 + -0.1

Combine like terms: 0.0 + -0.1 = -0.1
-2.166666667x + x2 = -0.1

The x term is -2.166666667x.  Take half its coefficient (-1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
-2.166666667x + 1.173611113 + x2 = -0.1 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667x + x2 = -0.1 + 1.173611113

Combine like terms: -0.1 + 1.173611113 = 1.073611113
1.173611113 + -2.166666667x + x2 = 1.073611113

Factor a perfect square on the left side:
(x + -1.083333334)(x + -1.083333334) = 1.073611113

Calculate the square root of the right side: 1.03615207

Break this problem into two subproblems by setting 
(x + -1.083333334) equal to 1.03615207 and -1.03615207.

Subproblem 1
x + -1.083333334 = 1.03615207

Simplifying
x + -1.083333334 = 1.03615207

Reorder the terms:
-1.083333334 + x = 1.03615207

Solving
-1.083333334 + x = 1.03615207

Solving for variable 'x'.

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

Add '1.083333334' to each side of the equation.
-1.083333334 + 1.083333334 + x = 1.03615207 + 1.083333334

Combine like terms: -1.083333334 + 1.083333334 = 0.000000000
0.000000000 + x = 1.03615207 + 1.083333334
x = 1.03615207 + 1.083333334

Combine like terms: 1.03615207 + 1.083333334 = 2.119485404
x = 2.119485404

Simplifying
x = 2.119485404

Subproblem 2
x + -1.083333334 = -1.03615207

Simplifying
x + -1.083333334 = -1.03615207

Reorder the terms:
-1.083333334 + x = -1.03615207

Solving
-1.083333334 + x = -1.03615207

Solving for variable 'x'.

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

Add '1.083333334' to each side of the equation.
-1.083333334 + 1.083333334 + x = -1.03615207 + 1.083333334

Combine like terms: -1.083333334 + 1.083333334 = 0.000000000
0.000000000 + x = -1.03615207 + 1.083333334
x = -1.03615207 + 1.083333334

Combine like terms: -1.03615207 + 1.083333334 = 0.047181264
x = 0.047181264

Simplifying
x = 0.047181264

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.119485404, 0.047181264}
Solution
x = {2.119485404, 0.047181264}