6x^2-3x-46=839

Solution for 6x^2-3x-46=839 equation:

Simplifying
6x2 + -3x + -46 = 839

Reorder the terms:
-46 + -3x + 6x2 = 839

Solving
-46 + -3x + 6x2 = 839

Solving for variable 'x'.

Reorder the terms:
-46 + -839 + -3x + 6x2 = 839 + -839

Combine like terms: -46 + -839 = -885
-885 + -3x + 6x2 = 839 + -839

Combine like terms: 839 + -839 = 0
-885 + -3x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-295 + -1x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-295 + -1x + 2x2)' equal to zero and attempt to solve:

Simplifying
-295 + -1x + 2x2 = 0

Solving
-295 + -1x + 2x2 = 0

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

Divide each side by '2'.
-147.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '147.5' to each side of the equation.
-147.5 + -0.5x + 147.5 + x2 = 0 + 147.5

Reorder the terms:
-147.5 + 147.5 + -0.5x + x2 = 0 + 147.5

Combine like terms: -147.5 + 147.5 = 0.0
0.0 + -0.5x + x2 = 0 + 147.5
-0.5x + x2 = 0 + 147.5

Combine like terms: 0 + 147.5 = 147.5
-0.5x + x2 = 147.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 147.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 147.5 + 0.0625

Combine like terms: 147.5 + 0.0625 = 147.5625
0.0625 + -0.5x + x2 = 147.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 147.5625

Calculate the square root of the right side: 12.147530613

Break this problem into two subproblems by setting 
(x + -0.25) equal to 12.147530613 and -12.147530613.

Subproblem 1
x + -0.25 = 12.147530613

Simplifying
x + -0.25 = 12.147530613

Reorder the terms:
-0.25 + x = 12.147530613

Solving
-0.25 + x = 12.147530613

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 12.147530613 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 12.147530613 + 0.25
x = 12.147530613 + 0.25

Combine like terms: 12.147530613 + 0.25 = 12.397530613
x = 12.397530613

Simplifying
x = 12.397530613

Subproblem 2
x + -0.25 = -12.147530613

Simplifying
x + -0.25 = -12.147530613

Reorder the terms:
-0.25 + x = -12.147530613

Solving
-0.25 + x = -12.147530613

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -12.147530613 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -12.147530613 + 0.25
x = -12.147530613 + 0.25

Combine like terms: -12.147530613 + 0.25 = -11.897530613
x = -11.897530613

Simplifying
x = -11.897530613

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.397530613, -11.897530613}
Solution
x = {12.397530613, -11.897530613}