Different Refractive indices in Anisotropic medium

In an anisotropic medium, if we consider the dielectric tensor to be diagonal and medium is isotropic in $$\mu$$ or ($$\mu = \mu_0$$). Then from fresnel equation we get a quadratic equation in 'n' (refractive index), where $$n^2 = \frac{c^2k^2}{\omega^2}$$, when the solutions for maxwell equations are plane wave of angular frequency $$\omega$$ and wave-vector $$\bar{k}$$. For a given a $$\bar{k}$$ and $$\omega$$, the value of n is fixed but how can we have two values of n, from Fresnel equation?

Fresnel Equation: