6x^2-17x+13x=20x^2-30

Solution for 6x^2-17x+13x=20x^2-30 equation:

Simplifying
6x2 + -17x + 13x = 20x2 + -30

Reorder the terms:
-17x + 13x + 6x2 = 20x2 + -30

Combine like terms: -17x + 13x = -4x
-4x + 6x2 = 20x2 + -30

Reorder the terms:
-4x + 6x2 = -30 + 20x2

Solving
-4x + 6x2 = -30 + 20x2

Solving for variable 'x'.

Reorder the terms:
30 + -4x + 6x2 + -20x2 = -30 + 20x2 + 30 + -20x2

Combine like terms: 6x2 + -20x2 = -14x2
30 + -4x + -14x2 = -30 + 20x2 + 30 + -20x2

Reorder the terms:
30 + -4x + -14x2 = -30 + 30 + 20x2 + -20x2

Combine like terms: -30 + 30 = 0
30 + -4x + -14x2 = 0 + 20x2 + -20x2
30 + -4x + -14x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
30 + -4x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -2x + -7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(15 + -2x + -7x2)' equal to zero and attempt to solve:

Simplifying
15 + -2x + -7x2 = 0

Solving
15 + -2x + -7x2 = 0

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

Divide each side by '-7'.
-2.142857143 + 0.2857142857x + x2 = 0

Move the constant term to the right:

Add '2.142857143' to each side of the equation.
-2.142857143 + 0.2857142857x + 2.142857143 + x2 = 0 + 2.142857143

Reorder the terms:
-2.142857143 + 2.142857143 + 0.2857142857x + x2 = 0 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + 0.2857142857x + x2 = 0 + 2.142857143
0.2857142857x + x2 = 0 + 2.142857143

Combine like terms: 0 + 2.142857143 = 2.142857143
0.2857142857x + x2 = 2.142857143

The x term is 0.2857142857x.  Take half its coefficient (0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
0.2857142857x + 0.02040816328 + x2 = 2.142857143 + 0.02040816328

Reorder the terms:
0.02040816328 + 0.2857142857x + x2 = 2.142857143 + 0.02040816328

Combine like terms: 2.142857143 + 0.02040816328 = 2.16326530628
0.02040816328 + 0.2857142857x + x2 = 2.16326530628

Factor a perfect square on the left side:
(x + 0.1428571429)(x + 0.1428571429) = 2.16326530628

Calculate the square root of the right side: 1.470804306

Break this problem into two subproblems by setting 
(x + 0.1428571429) equal to 1.470804306 and -1.470804306.

Subproblem 1
x + 0.1428571429 = 1.470804306

Simplifying
x + 0.1428571429 = 1.470804306

Reorder the terms:
0.1428571429 + x = 1.470804306

Solving
0.1428571429 + x = 1.470804306

Solving for variable 'x'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + x = 1.470804306 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + x = 1.470804306 + -0.1428571429
x = 1.470804306 + -0.1428571429

Combine like terms: 1.470804306 + -0.1428571429 = 1.3279471631
x = 1.3279471631

Simplifying
x = 1.3279471631

Subproblem 2
x + 0.1428571429 = -1.470804306

Simplifying
x + 0.1428571429 = -1.470804306

Reorder the terms:
0.1428571429 + x = -1.470804306

Solving
0.1428571429 + x = -1.470804306

Solving for variable 'x'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + x = -1.470804306 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + x = -1.470804306 + -0.1428571429
x = -1.470804306 + -0.1428571429

Combine like terms: -1.470804306 + -0.1428571429 = -1.6136614489
x = -1.6136614489

Simplifying
x = -1.6136614489

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3279471631, -1.6136614489}
Solution
x = {1.3279471631, -1.6136614489}