0=3x^4-14x^2-5

Solution for 0=3x^4-14x^2-5 equation:

Simplifying
0 = 3x4 + -14x2 + -5

Reorder the terms:
0 = -5 + -14x2 + 3x4

Solving
0 = -5 + -14x2 + 3x4

Solving for variable 'x'.

Combine like terms: 0 + 5 = 5
5 + 14x2 + -3x4 = -5 + -14x2 + 3x4 + 5 + 14x2 + -3x4

Reorder the terms:
5 + 14x2 + -3x4 = -5 + 5 + -14x2 + 14x2 + 3x4 + -3x4

Combine like terms: -5 + 5 = 0
5 + 14x2 + -3x4 = 0 + -14x2 + 14x2 + 3x4 + -3x4
5 + 14x2 + -3x4 = -14x2 + 14x2 + 3x4 + -3x4

Combine like terms: -14x2 + 14x2 = 0
5 + 14x2 + -3x4 = 0 + 3x4 + -3x4
5 + 14x2 + -3x4 = 3x4 + -3x4

Combine like terms: 3x4 + -3x4 = 0
5 + 14x2 + -3x4 = 0

Factor a trinomial.
(5 + -1x2)(1 + 3x2) = 0

Subproblem 1
Set the factor '(5 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Subproblem 2
Set the factor '(1 + 3x2)' equal to zero and attempt to solve:

Simplifying
1 + 3x2 = 0

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

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

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

Divide each side by '3'.
x2 = -0.3333333333

Simplifying
x2 = -0.3333333333

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-2.236067978, 2.236067978}