Answer
$x=-\frac{b}{3a}$
Work Step by Step
Step 1. For the given cubic curve, we have $y'=3ax^2+2bx+c$ and $y''=6ax+2b, a\ne0$
Step 2. To find possible inflection points, let $y''=0$; we get $x=-\frac{b}{3a}$
Step 3. We can test the $y''$ sign changes across this point as: $..(\pm)..(-\frac{b}{3a})..(\mp)..$; thus $x=-\frac{b}{3a}$ is an inflection point.
Step 4. We can not find more inflection points for this function.
