A quadratic equation will always have either two real, one real, or two complex (nonreal) solutions. Remember that the discriminant is the number $\displaystyle{{b}}^{{2}}-{4}{a}{c}\usepackage{cmbright}\Huge\$ , and that the solutions to a quadratic equation are given by the formula: $\displaystyle{x}=\frac{{-{b}\pm\sqrt{{{{b}}^{{2}}-{4}{a}{c}}}}}{{{2}{a}}}\usepackage{cmbright}\Huge\$