How to solve implicit function without using solve() function?

I searched online how to solve a implicit function in Matlab and here is the link it sent me to, https://www.mathworks.com/matlabcentral/answers/247461-best-way-to-solve-for-a-implicit-equation. I attempted to use the example in the link, but I get an error.

Exiting fzero: aborting search for an interval containing a sign change

because complex function value encountered during search.

(Function value at -0.28 is 15.0459-1.88983i.)

Check function or try again with a different starting value.

I was thinking about using the solve() function in Matlab, however I would need to purchase the symbolic math toolbox. :/ If there isn't a solution for this I may just re-write the equation in explicit form.

Attached is an image of the equation. I want to solve for 'f'.

func = (1 / sqrt(f5)) - 2 * log((eps / D) / 3.7) + ((2.51) / (Re * sqrt(f5)));
f5 = solve(func, 1)

Answer 1

[Star Strider]

If you have the Optimization Toolbox, use the fsolve function:

D = something;
Re = something_else;
func = @(f5) (1 / sqrt(f5)) - 2 * log((eps / D) / 3.7) + ((2.51) / (Re * sqrt(f5)));
f5 = fsolve(func, 1)

[Zachary Dunagan]

I don't have the Optimization Toolbox. Thanks for answering my question and letting me know which toolbox I need to get.

[Star Strider]

My pleasure.

That, and the Global Optimization Toolbox are both worth getting, for their robust optimization routines.