x^4-23x^2+90=0

Solution for x^4-23x^2+90=0 equation:

Simplifying
x4 + -23x2 + 90 = 0

Reorder the terms:
90 + -23x2 + x4 = 0

Solving
90 + -23x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x2)(18 + -1x2) = 0

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

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 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 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Subproblem 2
Set the factor '(18 + -1x2)' equal to zero and attempt to solve:

Simplifying
18 + -1x2 = 0

Solving
18 + -1x2 = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x2 = 0 + -18
-1x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-1x2 = -18

Divide each side by '-1'.
x2 = 18

Simplifying
x2 = 18

Take the square root of each side:
x = {-4.242640687, 4.242640687}
Solution
x = {-2.236067978, 2.236067978, -4.242640687, 4.242640687}