[tex]15a^2+45=0\qquad\text{subtract 45 from both sides}\\\\15a^2=-45\qquad\text{divide both sides by 15}\\\\a^2=-3<0\\\\\text{NO REAL SOLUTION}\\\\\text{in the complex set}\\\\a^2=-3\to a=\pm\sqrt{-3}\\\\a=\pm\sqrt{(-1)(3)}\\\\a=\pm\sqrt{-1}\cdot\sqrt3\\\\\boxed{a=-i\sqrt3\ \vee\ a=i\sqrt3}\\\\------------------\\\\i=\sqrt{-1}[/tex]
