3+8x^2-3x^4=0

Solution for 3+8x^2-3x^4=0 equation:

Simplifying
3 + 8x2 + -3x4 = 0

Solving
3 + 8x2 + -3x4 = 0

Solving for variable 'x'.

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

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

Simplifying
3 + -1x2 = 0

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

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

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

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
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 = {-1.732050808, 1.732050808}