Minimum of $a$ for $a^2+2b^2+c^2+ab-bc-ac=1$

[anemone]

Let $a,\,b,\,c$ be real numbers such that $a^2+2b^2+c^2+ab-bc-ac=1$. Find the minimum possible value of $a$.

 

[anemone]

Hint:

Spoiler

Discriminant of quadratic equation helps...:)