We know [tex]y=6[/tex] which means we already have one solution.
Plug in 6 in the first equation where y-terms are and solve for x.
[tex]
6=6^2(x^2-3) \\
1=6(x^2-3) \\
1=6x^2-18 \\
6x^2=19 \\
x^2=\frac{19}{6} \\
x_{1,2}=\boxed{\pm\sqrt{\frac{19}{6}}}
[/tex]
Hope this helps.
