1200=500/x + 500/x^2 + 500/x^3 + 500/x^4

Answer 1

1200 = 500(1/x+1/x^2+1/x^3+1/x^4)
12/5 x^4 - x^3 - x^2 - x - 1 = 0

Now, quartics are tough to solve algebraically. Use your favorite numerical method to crack this one.