General Form for Intersection of Quadratic with Natural Log Function

32 Views Asked by At

Given $x. a_0, a_1, a_2, b\in\mathbb{R}$ is there a general solution to the equation:

$a_0+a_1x+a_2x^2=b\ln(x)$

I am aware of the connection between this sort of equation and the Lambert W function, but have not been able to find a generic solution.