Solve the inequation: $\;$ $3x^2 - 7x -6 < 0$
Given inequation: $\;$ $3x^2 - 7x - 6 < 0$
i.e. $\;$ $\left(3x + 2\right) \left(x - 3\right) < 0$
i.e. $\;$ $3x + 2 < 0 \; \cap \; x - 3 > 0$ $\;$ OR $\;$ $3x + 2 > 0 \; \cap \; x - 3 < 0$
i.e. $\;$ $x < \dfrac{-2}{3} \; \cap \; x > 3$ $\;$ which is not possible
OR $\;$ $x > \dfrac{-2}{3} \; \cap \; x < 3$ $\implies$ $x \in \left(\dfrac{-2}{3}, 3\right)$
$\therefore \;$ The solution is $\;$ $x \in \left(\dfrac{-2}{3}, 3\right)$