5x^4-24x^2+19=0

Solution for 5x^4-24x^2+19=0 equation:

Simplifying
5x4 + -24x2 + 19 = 0

Reorder the terms:
19 + -24x2 + 5x4 = 0

Solving
19 + -24x2 + 5x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x2)(19 + -5x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(19 + -5x2) = 0

Subproblem 1
Set the factor '(19 + -5x2)' equal to zero and attempt to solve:

Simplifying
19 + -5x2 = 0

Solving
19 + -5x2 = 0

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

Add '-19' to each side of the equation.
19 + -19 + -5x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -5x2 = 0 + -19
-5x2 = 0 + -19

Combine like terms: 0 + -19 = -19
-5x2 = -19

Divide each side by '-5'.
x2 = 3.8

Simplifying
x2 = 3.8

Take the square root of each side:
x = {-1.949358869, 1.949358869}
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {-1.949358869, 1.949358869, -1, 1}