jjbyram wrote:

exp(W*(1/(x*(x+1))^.5))=(2*J+1)*(2*x+1)

So above same as:

eW / SQRT(x^2 + x) = (2J + 1)(2x + 1)

Let A = eW and B = 2J +1; then:

A / SQRT(x^2 + x) = B(2x + 1)

Rewrite:

A / [B(2x + 1)] = SQRT(x^2 + x)

Square both sides:

A^2 / [B^2 (4x^2 + 4x + 1)] = x^2 + x

Rewrite:

A^2 / B^2 = (4x^2 + 4x + 1)(x^2 + x)

Do right side multiplication; simplify:

A^2 / B^2 = 4x^4 + 8x^3 + 5x^2 + x

I guess you can "nicely" wrap up this way:

Let K = A^2 / B^2

4x^4 + 8x^3 + 5x^2 + x - K = 0

Well, what can I say?! No cute quadratic for you today

Anyway, seems to work: tested it "guessed at" data;

why don't you try it out...

http://www.numberempire.com/equationsolver.php