= Solution
At an <equilibrium point> of the <Rössler system>, $y=-z$, $x=az$, and $az^2-cz+a=0$. Hence
$$
\boxed{z_\pm=\frac{c\pm\sqrt{c^2-4a^2}}{2a},\qquad
(x_\pm,y_\pm,z_\pm)=(az_\pm,-z_\pm,z_\pm).}
$$
There are two distinct real <equilibrium points> only if $c>2a$; they merge if $c=2a$ and there are none if $c<2a$. Positivity of $a,c$ alone does not guarantee two. Under the later limits, the nearer one is $(x_-,y_-,z_-)\simeq(a^2/c,-a/c,a/c)$, while $(x_+,y_+,z_+)\simeq(c,-c/a,c/a)$.
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