-5000x^4+3500x^2+3000=0

Solution for -5000x^4+3500x^2+3000=0 equation:

Simplifying
-5000x4 + 3500x2 + 3000 = 0

Reorder the terms:
3000 + 3500x2 + -5000x4 = 0

Solving
3000 + 3500x2 + -5000x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '500'.
500(6 + 7x2 + -10x4) = 0

Factor a trinomial.
500((6 + -5x2)(1 + 2x2)) = 0

Ignore the factor 500.
Subproblem 1
Set the factor '(6 + -5x2)' equal to zero and attempt to solve:

Simplifying
6 + -5x2 = 0

Solving
6 + -5x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x2 = 0 + -6
-5x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-5x2 = -6

Divide each side by '-5'.
x2 = 1.2

Simplifying
x2 = 1.2

Take the square root of each side:
x = {-1.095445115, 1.095445115}
Subproblem 2
Set the factor '(1 + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + 2x2 = 0

Solving
1 + 2x2 = 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 + 2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x2 = 0 + -1
2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
2x2 = -1

Divide each side by '2'.
x2 = -0.5

Simplifying
x2 = -0.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-1.095445115, 1.095445115}