Find $x$ if $(7+4\sqrt 3)^{x^2-8}+(7-4\sqrt 3)^{x^2-8}=14$ 

Known that:
    $$(7+4\sqrt 3)^{x^2-8}+(7-4\sqrt 3)^{x^2-8}=14$$
    What is the value of $x$



Note that $$(7+4 \sqrt{3}) \cdot (7-4\sqrt{3}) = 49-48 =1$$
