24x^4+x^2-3=0

Solution for 24x^4+x^2-3=0 equation:

Simplifying
24x4 + x2 + -3 = 0

Reorder the terms:
-3 + x2 + 24x4 = 0

Solving
-3 + x2 + 24x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -8x2)(1 + -3x2) = 0

Subproblem 1
Set the factor '(-3 + -8x2)' equal to zero and attempt to solve:

Simplifying
-3 + -8x2 = 0

Solving
-3 + -8x2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -8x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8x2 = 0 + 3
-8x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-8x2 = 3

Divide each side by '-8'.
x2 = -0.375

Simplifying
x2 = -0.375

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 + -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

Take the square root of each side:
x = {-0.577350269, 0.577350269}
Solution
x = {-0.577350269, 0.577350269}