Sorry....misposted the original question...

350/(400*50^(3/2)) = X+(50+X)^(3/2)

Thanks for the help

Wow

I evaluated the left side to get .002475

I changed this to a function to read

f(x) = x + (x+50)^1.5 - .002475

and used my homemade Newton's Formula program.
After about 15 iterations I got x = -38.58159

which when substituted into the original equation makes the left side differ from the right side by .0000418

which is about as good an answer as we can get.

BTW, this level of equation is way beyond anything you would find to about first year university math.
I did not show you how to do, but merely gave you the answer.

Thanks for the challenge but are you sure you typed it correctly??