[tex]\frac{1}{x}-\frac{x}{2}=3\\\\\frac{2-x^2}{2x}=3; \ x\neq0\\\\2-x^2=6x\\\\-x^2-6x+2=0 \ \ |\cdot(-1)\\\\x^2+6x-2=0\\\\a=1, \ b=6, \ c=-2\\\\\Delta=b^2-4ac\rightarrow6^2-4\cdot1\cdot(-2)=36+8=44\\\\\sqrt{\Delta}=\sqrt{44}=\sqrt{4\cdot11}=2\sqrt{11}\\\\x_1=\frac{-b-\sqrt{\Delta}}{2a}\rightarrow\frac{-6-2\sqrt{11}}{2}=-3-\sqrt{11}\\\\x_2=\frac{-b+\sqrt{\Delta}}{2a}\rightarrow\frac{-6+2\sqrt{11}}{2}=-3+\sqrt{11}[/tex]