-14X^2+24+X^4=0

Solution for -14X^2+24+X^4=0 equation:

Simplifying
-14X2 + 24 + X4 = 0

Reorder the terms:
24 + -14X2 + X4 = 0

Solving
24 + -14X2 + X4 = 0

Solving for variable 'X'.

Factor a trinomial.
(2 + -1X2)(12 + -1X2) = 0

Subproblem 1
Set the factor '(2 + -1X2)' equal to zero and attempt to solve:

Simplifying
2 + -1X2 = 0

Solving
2 + -1X2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1X2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1X2 = 0 + -2
-1X2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1X2 = -2

Divide each side by '-1'.
X2 = 2

Simplifying
X2 = 2

Take the square root of each side:
X = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(12 + -1X2)' equal to zero and attempt to solve:

Simplifying
12 + -1X2 = 0

Solving
12 + -1X2 = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1X2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1X2 = 0 + -12
-1X2 = 0 + -12

Combine like terms: 0 + -12 = -12
-1X2 = -12

Divide each side by '-1'.
X2 = 12

Simplifying
X2 = 12

Take the square root of each side:
X = {-3.464101615, 3.464101615}
Solution
X = {-1.414213562, 1.414213562, -3.464101615, 3.464101615}