[tex]3x^2+12x-1\\\\a=3;\ b=12;\ c=-1\\\\\Delta=b^2-4ac\to\Delta=12^2-4\cdot3\cdot(-1)=144+12=156\\\\x=\frac{-b\pm\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{156}=\sqrt{4\cdot39}=\sqrt4\cdot\sqrt{39}=2\sqrt{39}\\\\x=\frac{-12\pm2\sqrt{39}}{2\cdot3}=\frac{-6\pm\sqrt{39}}{3}\\\\3x^2+12x-1=3(x-\frac{-6-\sqrt{39}}{3})(x-\frac{-6+\sqrt{39}}{3})\\\\=\boxed{3(x+\frac{6+\sqrt{39}}{3})(x+\frac{6-\sqrt{39}}{3})}[/tex]
