#include <boost/math/tools/roots.hpp>
double solve_for_F(double var_epsilon_D, double var_Re, double starting_guess=0.5)
    using namespace boost::math;
    tools::eps_tolerance<double> tol(std::numeric_limits<double>::digits / 2);
    const int maximumIterations = 1000;
    boost::uintmax_t maxIter(maximumIterations); //maximum number of attempts
    try{
        const std::pair<double, double> Result = tools::bracket_and_solve_root(
            [var_epsilon_D,var_Re](double var_f) -> double {
                return (1.0/sqrt(f))+2.0*log10((var_epsilon_D/3.7)+(2.5/(var_Re*sqrt(f))));
            }
            , starting_guess, 2.0, false, tol, maxIter, optim_policy());
        if (maxIter >= maximumIterations)
            return 0.0; //failed to find
        return (Result.first + Result.second) / 2.0;
    }
    catch (evaluation_error) {
        return 0.0; // Evaluation Error
    }
    catch (std::underflow_error) {
        return 0.0; // Underflow Error
    }
    catch (std::underflow_error) {
        return 0.0; // Overflow Error
    }
    catch (std::domain_error) {
        return 0.0; // Domain Error
    }
}

in qt c++

Qt is a toolkit/function library. It is not a language, and there is no such thing as "Qt C++".
Your question seems to be a pure C++ one. Qt does not address this area.