0=5u^4-28u^2+39

Solution for 0=5u^4-28u^2+39 equation:

Simplifying
0 = 5u4 + -28u2 + 39

Reorder the terms:
0 = 39 + -28u2 + 5u4

Solving
0 = 39 + -28u2 + 5u4

Solving for variable 'u'.

Combine like terms: 0 + -39 = -39
-39 + 28u2 + -5u4 = 39 + -28u2 + 5u4 + -39 + 28u2 + -5u4

Reorder the terms:
-39 + 28u2 + -5u4 = 39 + -39 + -28u2 + 28u2 + 5u4 + -5u4

Combine like terms: 39 + -39 = 0
-39 + 28u2 + -5u4 = 0 + -28u2 + 28u2 + 5u4 + -5u4
-39 + 28u2 + -5u4 = -28u2 + 28u2 + 5u4 + -5u4

Combine like terms: -28u2 + 28u2 = 0
-39 + 28u2 + -5u4 = 0 + 5u4 + -5u4
-39 + 28u2 + -5u4 = 5u4 + -5u4

Combine like terms: 5u4 + -5u4 = 0
-39 + 28u2 + -5u4 = 0

Factor a trinomial.
(-3 + u2)(13 + -5u2) = 0

Subproblem 1
Set the factor '(-3 + u2)' equal to zero and attempt to solve:

Simplifying
-3 + u2 = 0

Solving
-3 + u2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + u2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + u2 = 0 + 3
u2 = 0 + 3

Combine like terms: 0 + 3 = 3
u2 = 3

Simplifying
u2 = 3

Take the square root of each side:
u = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(13 + -5u2)' equal to zero and attempt to solve:

Simplifying
13 + -5u2 = 0

Solving
13 + -5u2 = 0

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

Add '-13' to each side of the equation.
13 + -13 + -5u2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -5u2 = 0 + -13
-5u2 = 0 + -13

Combine like terms: 0 + -13 = -13
-5u2 = -13

Divide each side by '-5'.
u2 = 2.6

Simplifying
u2 = 2.6

Take the square root of each side:
u = {-1.61245155, 1.61245155}
Solution
u = {-1.732050808, 1.732050808, -1.61245155, 1.61245155}