[tex]3x^2+4x+5=0 \\ x_{12} = \frac{-4\; \pm \; \sqrt{16 - 4*3*5} }{2*3}= \frac{-4\; \pm \; \sqrt{16 - 60} }{6} =\frac{-4\; \pm \; \sqrt{-44} }{6}= \\ \\ =\frac{-4\; \pm \; 2\sqrt{-11} }{6}=\frac{-2\; \pm \; i\sqrt{11} }{3} = -\frac{2}{3} \; \pm \; \frac{ \sqrt{11} }{3}i \\ \\ x_1 =\boxed{ -\frac{2}{3} \;+ \; \frac{ \sqrt{11} }{3}i }\\ \\ x_2 =\boxed{ -\frac{2}{3} \;- \; \frac{ \sqrt{11} }{3}i }[/tex]
