4a^4-17a^2+18=0

Solution for 4a^4-17a^2+18=0 equation:

Simplifying
4a4 + -17a2 + 18 = 0

Reorder the terms:
18 + -17a2 + 4a4 = 0

Solving
18 + -17a2 + 4a4 = 0

Solving for variable 'a'.

Factor a trinomial.
(2 + -1a2)(9 + -4a2) = 0

Factor a difference between two squares.
(2 + -1a2)((3 + 2a)(3 + -2a)) = 0

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

Simplifying
2 + -1a2 = 0

Solving
2 + -1a2 = 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 + -1a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a2 = 0 + -2
-1a2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1a2 = -2

Divide each side by '-1'.
a2 = 2

Simplifying
a2 = 2

Take the square root of each side:
a = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(3 + 2a)' equal to zero and attempt to solve:

Simplifying
3 + 2a = 0

Solving
3 + 2a = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2a = 0 + -3
2a = 0 + -3

Combine like terms: 0 + -3 = -3
2a = -3

Divide each side by '2'.
a = -1.5

Simplifying
a = -1.5
Subproblem 3
Set the factor '(3 + -2a)' equal to zero and attempt to solve:

Simplifying
3 + -2a = 0

Solving
3 + -2a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2a = 0 + -3
-2a = 0 + -3

Combine like terms: 0 + -3 = -3
-2a = -3

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Solution
a = {-1.414213562, 1.414213562, -1.5, 1.5}