The potential energy of an object is given by  $U\left(x\right)=2x^2-3x^3$, where  $U$ is in joules and  $x$ is in meters. 

The state of equilibrium is attained when the force acting on the particle is zero, 

So $F=\frac{-dU}{dx}$=0 at x=0 and $x=\frac{4}{9}$.

To find the equilibrium is stable or unstable we need $\frac{d^{2}U}{d{x}^2}$

$\frac{d^{2}U}{d{x}^2}=4-18x$.

So $\frac{d^{2}U}{d{x}^2}$ will be positive for x=0 ( stable equilibrium). and $\frac{d^{2}U}{d{x}^2}$will be negative for $x=\frac{4}{9}$(unstable equilibrium).