How can I solve this summations math problem involving polynomials?

[Big-Daddy]

$$kx^n = \sum_{j=1}^n ({(j-k)x^{n-j}d_j})$$

d_j is a constant but dependent on j, i.e. independent of x. k is an integer varying between n (which is also an integer) and 0 but it can be assumed that k can equal neither n nor 0.

Is there any way of solving this generally for x? Or is a polynomial the best I can do?

 

[ShayanJ]

You are in fact asking for exact ways of solving polynomial equations.As far as I know,there is no general formula encompassing polynomials of any degree.Take a look at here.