Answer:
[tex]\mathrm{x=-1\pm\sqrt{2}i}[/tex]
Step-by-step explanation:
[tex]\mathrm{2x^2+4x+6=0}\\\\\mathrm{x_{1,\:2}=\frac{-4\pm \sqrt{4^2-4\cdot \:2\cdot \:6}}{2\cdot \:2}}\\\\\mathrm{x_1=\frac{-4+4\sqrt{2}i}{2\cdot \:2},\:x_2=\frac{-4-4\sqrt{2}i}{2\cdot \:2}}\\\\\mathrm{x=-1\pm\sqrt{2}i}[/tex]