3(3x^2-5)=x

Solution for 3(3x^2-5)=x equation:

Simplifying
3(3x2 + -5) = x

Reorder the terms:
3(-5 + 3x2) = x
(-5 * 3 + 3x2 * 3) = x
(-15 + 9x2) = x

Solving
-15 + 9x2 = x

Solving for variable 'x'.

Reorder the terms:
-15 + -1x + 9x2 = x + -1x

Combine like terms: x + -1x = 0
-15 + -1x + 9x2 = 0

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

Divide each side by '9'.
-1.666666667 + -0.1111111111x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -0.1111111111x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -0.1111111111x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -0.1111111111x + x2 = 0 + 1.666666667
-0.1111111111x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-0.1111111111x + x2 = 1.666666667

The x term is -0.1111111111x.  Take half its coefficient (-0.05555555555).
Square it (0.003086419752) and add it to both sides.

Add '0.003086419752' to each side of the equation.
-0.1111111111x + 0.003086419752 + x2 = 1.666666667 + 0.003086419752

Reorder the terms:
0.003086419752 + -0.1111111111x + x2 = 1.666666667 + 0.003086419752

Combine like terms: 1.666666667 + 0.003086419752 = 1.669753086752
0.003086419752 + -0.1111111111x + x2 = 1.669753086752

Factor a perfect square on the left side:
(x + -0.05555555555)(x + -0.05555555555) = 1.669753086752

Calculate the square root of the right side: 1.292189261

Break this problem into two subproblems by setting 
(x + -0.05555555555) equal to 1.292189261 and -1.292189261.

Subproblem 1
x + -0.05555555555 = 1.292189261

Simplifying
x + -0.05555555555 = 1.292189261

Reorder the terms:
-0.05555555555 + x = 1.292189261

Solving
-0.05555555555 + x = 1.292189261

Solving for variable 'x'.

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

Add '0.05555555555' to each side of the equation.
-0.05555555555 + 0.05555555555 + x = 1.292189261 + 0.05555555555

Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000
0.00000000000 + x = 1.292189261 + 0.05555555555
x = 1.292189261 + 0.05555555555

Combine like terms: 1.292189261 + 0.05555555555 = 1.34774481655
x = 1.34774481655

Simplifying
x = 1.34774481655

Subproblem 2
x + -0.05555555555 = -1.292189261

Simplifying
x + -0.05555555555 = -1.292189261

Reorder the terms:
-0.05555555555 + x = -1.292189261

Solving
-0.05555555555 + x = -1.292189261

Solving for variable 'x'.

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

Add '0.05555555555' to each side of the equation.
-0.05555555555 + 0.05555555555 + x = -1.292189261 + 0.05555555555

Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000
0.00000000000 + x = -1.292189261 + 0.05555555555
x = -1.292189261 + 0.05555555555

Combine like terms: -1.292189261 + 0.05555555555 = -1.23663370545
x = -1.23663370545

Simplifying
x = -1.23663370545

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.34774481655, -1.23663370545}