How would you solve this equation?
$$\frac{1^4}{2\sqrt{x} + 1} + \frac{2^4}{2\sqrt{x} + 3} + \frac{3^4}{2\sqrt{x} + 5} + \frac{4^4}{2\sqrt{x} + 7} = 50$$
I know the answer is $1/4$, and I know you can simply solve this by computing LCM, but it must have a simpler solution. I tried to simplify all as a summation like $\sum_{n=0}^{n=3} \frac{(n+1)^4}{2\sqrt{x}+2n+1} = 50$ but I don't really figure out how to continue from this, could you help me?
Thanks in advance