$2x^{2} - 7x - 9 = 0$
$\Leftrightarrow 2x^{2} + 2x - 9x - 9 = 0$
$\Leftrightarrow 2x(x + 1) - 9(x + 1) = 0$
$\Leftrightarrow (x + 1).(2x - 9) = 0$
$\Leftrightarrow \left[ \begin{array}{l}x+1=0\\2x-9=0\end{array} \right.$
$\Leftrightarrow \left[ \begin{array}{l}x=-1\\x=\dfrac{9}{2}\end{array} \right.$
