Разложите на множители квадратный трехчлен 6x^2+x-12.

\[6x^{2} + x - 12\]

\[D = 1 + 288 = 289\]

\[x_{1} = \frac{- 1 + 17}{12} = \frac{16}{12} = \frac{4}{3};\]

\[x_{2} = \frac{- 1 - 17}{12} = - \frac{18}{12} = - \frac{3}{2}.\]

\[6x^{2} + x - 12 = 6 \cdot \left( x + \frac{3}{2} \right)\left( x - \frac{4}{3} \right) =\]

\[= (2x + 3)(3x - 4).\]