[tex]f(x)=6x^2-x-12\\\\a=6\qquad b=-1\qquad c=-12\\\\\\
\Delta=b^2-4\cdot a\cdot c=(-1)^2-4\cdot6\cdot(-12)=1+288=289\\\\\sqrt{\Delta}=\sqrt{289}=17\ \textgreater \ 0\\\\\\
x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-(-1)-17}{2\cdot6}=\dfrac{1-17}{12}=\dfrac{-16}{12}=-\dfrac{4}{3}\\\\\\
x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-(-1)+17}{2\cdot6}=\dfrac{1+17}{12}=\dfrac{18}{12}=\dfrac{3}{2}\\\\\\\\
[/tex]
[tex]f(x)=a(x-x_1)(x-x_2)=6(x-(-\dfrac{4}{3}))(x-\dfrac{3}{2})=6(x+\dfrac{4}{3})(x-\dfrac{3}{2})=\\\\\\=
3\cdot2(x+\dfrac{4}{3})(x-\dfrac{3}{2})=3(x+\dfrac{4}{3})\cdot2(x-\dfrac{3}{2})=
\boxed{(3x+4)(2x-3)}[/tex]
