Answer:
[tex]x=\frac{12+\sqrt{138}}{6}\:\:or\:\:x=\frac{12-\sqrt{138}}{6}[/tex]
Step-by-step explanation:
[tex]f(x)=6x^2-24x+1\\\\0=6x^2-24x+1\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-24)\pm\sqrt{(-24)^2-4(6)(1)}}{2(6)}\\ \\x=\frac{24\pm\sqrt{576-24}}{12}\\\\x=\frac{24\pm2\sqrt{138}}{12}\\\\x=\frac{12\pm\sqrt{138}}{6}[/tex]