$f(x) = 3\ln|x−1|−1/2x^2−x$
I tried to get this function on a graph calculator and beside revealing the intersection point $(0, 0)$, it also showed and interesting point that approximates to $x = 4.123$, yet doing this algebraically I can see why it yields $(0, 0)$ but I'm having trouble to figure out the other $x$ intercept to that second point or even why should I bother with it in the first place, I'm sure that analyzing the growth gives a clear picture of what's going on with the function. I tried to treat it with the quadratic formula but I'm sure I'm off the rails with the result, if I can gain any insight with how develop the solutions to $3\ln|x−1|−1/2x^2 − x = 0$ it would be very helpful.