Given that $a$, $b$ and $c$ are real numbers such that $b^2 = 4ac$ and $a > 0$. The maximal possible set $D \subseteq \mathbb{R}$ on which the function $f : D \to \mathbb{R}$ given by $f(x) = \log\left(ax^3 + (a+b)x^2 + (b+c)x + c\right)$ is defined, is