[tex]x^2-6x+6=0\\\\a=1;\ b=-6;\ c=6\\\Delta=b^2-4ac\\\\\Delta=(-6)^2-4\cdot1\cdot6=36-24=12 \ \textgreater \ 0\\\\then\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{12}=\sqrt{4\cdot3}=\sqrt4\cdot\sqrt3=2\sqrt3\\\\x_1=\dfrac{6-2\sqrt3}{2\cdot1}=\dfrac{6-2\sqrt3}{2}=\boxed{3-\sqrt3}\\\\x_2=\dfrac{6+2\sqrt3}{2\cdot1}=\dfrac{6+2\sqrt3}{2}=\boxed{3+\sqrt3}[/tex]
