Not sure what the problem is. And why are you asking about fsolve?
a = 1.66;
b = 0.000127;
c = 2.5;
d = 0.000423;
g = 9.81;
syms x
solve (a/sqrt(g*x*b) == 6 + c*log(x/(c*d)),x)
Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.
> In solve (line 304)
ans =
3.2523216595041553985081838768663
No symbolic solution was found, so it used vpasolve to find a numerical solution. wtp?
If you wanted a fully general analytical solution, tough luck. It is terribly easy to write an equation that has no analytcal solution. In fact, it seems you just did it.
Note my use of sqrt, insead of raising to a fractional power. Far easier to read.
