I'm wondering if there exists a closed-form or analytic expression for the roots of an equation of the form
$ax^2 + bx + c\log x=0.$
considering the natural $\log$. Wolfram alpha is leading me to expressions involving the Lambert W (product log) function when I include either the quadratic term or the linear term (but not both) and analytic approximations when I supply real values for the coefficients.
This is OK, but does a more general solution exist in terms of the coefficients?