It's a quadratic equation in disguise. If you let [tex]y=x^{-1}[/tex], then [tex]y^2=x^{-2}[/tex], and we can rewrite the equation as
[tex]5y^2-17y+6=0[/tex]
Solve for [tex]y[/tex] however you like; we get [tex]y=\dfrac25[/tex] and [tex]y=3[/tex].
But we want to solve for [tex]x[/tex], so we have
[tex]y=x^{-1}=\dfrac25\implies x=\dfrac52[/tex]
[tex]y=x^{-1}=3\implies x=\dfrac13[/tex]
