2x^4=3x^2+5

Solution for 2x^4=3x^2+5 equation:

Simplifying
2x4 = 3x2 + 5

Reorder the terms:
2x4 = 5 + 3x2

Solving
2x4 = 5 + 3x2

Solving for variable 'x'.

Reorder the terms:
-5 + -3x2 + 2x4 = 5 + 3x2 + -5 + -3x2

Reorder the terms:
-5 + -3x2 + 2x4 = 5 + -5 + 3x2 + -3x2

Combine like terms: 5 + -5 = 0
-5 + -3x2 + 2x4 = 0 + 3x2 + -3x2
-5 + -3x2 + 2x4 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-5 + -3x2 + 2x4 = 0

Factor a trinomial.
(-1 + -1x2)(5 + -2x2) = 0

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

Simplifying
-1 + -1x2 = 0

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

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

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

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

Simplifying
x2 = -1

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 '(5 + -2x2)' equal to zero and attempt to solve:

Simplifying
5 + -2x2 = 0

Solving
5 + -2x2 = 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 + -2x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x2 = 0 + -5
-2x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2x2 = -5

Divide each side by '-2'.
x2 = 2.5

Simplifying
x2 = 2.5

Take the square root of each side:
x = {-1.58113883, 1.58113883}
Solution
x = {-1.58113883, 1.58113883}