The domain will exclude values for which the value of the denominator is 0. Factoring $\displaystyle{2}{{x}}^{{2}}-{9}{x}-{5}\usepackage{cmbright}\Huge\$ as $\displaystyle{\left({2}{x}+{1}\right)}{\left({x}-{5}\right)}\usepackage{cmbright}\Huge\$ , you found that the value of the denominator will be 0 when $\displaystyle{x}=-\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$ and 5. These values are excluded from the domain.