20a^4+13a^2-15=0

Solution for 20a^4+13a^2-15=0 equation:

Simplifying
20a4 + 13a2 + -15 = 0

Reorder the terms:
-15 + 13a2 + 20a4 = 0

Solving
-15 + 13a2 + 20a4 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -4a2)(3 + -5a2) = 0

Subproblem 1
Set the factor '(-5 + -4a2)' equal to zero and attempt to solve:

Simplifying
-5 + -4a2 = 0

Solving
-5 + -4a2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4a2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4a2 = 0 + 5
-4a2 = 0 + 5

Combine like terms: 0 + 5 = 5
-4a2 = 5

Divide each side by '-4'.
a2 = -1.25

Simplifying
a2 = -1.25

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + -5a2)' equal to zero and attempt to solve:

Simplifying
3 + -5a2 = 0

Solving
3 + -5a2 = 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 + -5a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5a2 = 0 + -3
-5a2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5a2 = -3

Divide each side by '-5'.
a2 = 0.6

Simplifying
a2 = 0.6

Take the square root of each side:
a = {-0.774596669, 0.774596669}
Solution
a = {-0.774596669, 0.774596669}