3x^2-1=6x

Solution for 3x^2-1=6x equation:

Simplifying
3x2 + -1 = 6x

Reorder the terms:
-1 + 3x2 = 6x

Solving
-1 + 3x2 = 6x

Solving for variable 'x'.

Reorder the terms:
-1 + -6x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-1 + -6x + 3x2 = 0

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

Divide each side by '3'.
-0.3333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -2x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -2x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + 0.3333333333
-2x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-2x + x2 = 0.3333333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 0.3333333333 + 1

Reorder the terms:
1 + -2x + x2 = 0.3333333333 + 1

Combine like terms: 0.3333333333 + 1 = 1.3333333333
1 + -2x + x2 = 1.3333333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.3333333333

Calculate the square root of the right side: 1.154700538

Break this problem into two subproblems by setting 
(x + -1) equal to 1.154700538 and -1.154700538.

Subproblem 1
x + -1 = 1.154700538

Simplifying
x + -1 = 1.154700538

Reorder the terms:
-1 + x = 1.154700538

Solving
-1 + x = 1.154700538

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.154700538 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.154700538 + 1
x = 1.154700538 + 1

Combine like terms: 1.154700538 + 1 = 2.154700538
x = 2.154700538

Simplifying
x = 2.154700538

Subproblem 2
x + -1 = -1.154700538

Simplifying
x + -1 = -1.154700538

Reorder the terms:
-1 + x = -1.154700538

Solving
-1 + x = -1.154700538

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.154700538 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.154700538 + 1
x = -1.154700538 + 1

Combine like terms: -1.154700538 + 1 = -0.154700538
x = -0.154700538

Simplifying
x = -0.154700538

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.154700538, -0.154700538}