Welcome to the forum.
If one of B, D, G, L, N is a multiple of the rest, then this problem reduces to finding roots of a polynomial. For example, suppose that B = d * D = g * G = l * L = n * N for some positive integer d, g, l, n. Then . So, the equation becomes for .
Do you need to solve this equation symbolically or numerically? Is there some background knowledge that you need to use? Also, depending on these answers, you need to post this question to the right forum (this one is about discrete mathematics).