6=a^4+2

Solution for 6=a^4+2 equation:

Simplifying
6 = a4 + 2

Reorder the terms:
6 = 2 + a4

Solving
6 = 2 + a4

Solving for variable 'a'.

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

Add '-1a4' to each side of the equation.
6 + -1a4 = 2 + a4 + -1a4

Combine like terms: a4 + -1a4 = 0
6 + -1a4 = 2 + 0
6 + -1a4 = 2

Add '-6' to each side of the equation.
6 + -6 + -1a4 = 2 + -6

Combine like terms: 6 + -6 = 0
0 + -1a4 = 2 + -6
-1a4 = 2 + -6

Combine like terms: 2 + -6 = -4
-1a4 = -4

Divide each side by '-1'.
a4 = 4

Simplifying
a4 = 4

Reorder the terms:
-4 + a4 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + a4 = 0

Factor a difference between two squares.
(2 + a2)(-2 + a2) = 0

Subproblem 1
Set the factor '(2 + a2)' equal to zero and attempt to solve:

Simplifying
2 + a2 = 0

Solving
2 + a2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a2 = 0 + -2
a2 = 0 + -2

Combine like terms: 0 + -2 = -2
a2 = -2

Simplifying
a2 = -2

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 '(-2 + a2)' equal to zero and attempt to solve:

Simplifying
-2 + a2 = 0

Solving
-2 + a2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + a2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + a2 = 0 + 2
a2 = 0 + 2

Combine like terms: 0 + 2 = 2
a2 = 2

Simplifying
a2 = 2

Take the square root of each side:
a = {-1.414213562, 1.414213562}
Solution
a = {-1.414213562, 1.414213562}