54x^4-3x^2-1=0

Solution for 54x^4-3x^2-1=0 equation:

Simplifying
54x4 + -3x2 + -1 = 0

Reorder the terms:
-1 + -3x2 + 54x4 = 0

Solving
-1 + -3x2 + 54x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -9x2)(1 + -6x2) = 0

Subproblem 1
Set the factor '(-1 + -9x2)' equal to zero and attempt to solve:

Simplifying
-1 + -9x2 = 0

Solving
-1 + -9x2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -9x2 = 0 + 1

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

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

Divide each side by '-9'.
x2 = -0.1111111111

Simplifying
x2 = -0.1111111111

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + -6x2)' equal to zero and attempt to solve:

Simplifying
1 + -6x2 = 0

Solving
1 + -6x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -6x2 = 0 + -1

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

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

Divide each side by '-6'.
x2 = 0.1666666667

Simplifying
x2 = 0.1666666667

Take the square root of each side:
x = {-0.408248291, 0.408248291}
Solution
x = {-0.408248291, 0.408248291}