Answer :
[tex]x^2-6x+6=0\\
x^2-6x+9-3=0\\
(x-3)^2=3\\
x-3=\sqrt 3 \vee x-3=-\sqrt3\\
x=3+\sqrt3 \vee x=3-\sqrt3[/tex]
[tex]x^2-6x+6=0 \\ \\a=1, \ \ b=-6, \ \ c=6 \\\\\Delta =b^2-4ac = (-6)^2 -4\cdot1\cdot 6 = 36-24=12\\\\\sqrt{\Delta }=\sqrt{12}=\sqrt{4\cdot 3}=2\sqrt{3}\\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{6-2\sqrt{3}}{2 }=\frac{2( 3- \sqrt{3})}{2}= 3- \sqrt{3}\\\\x_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{6+2\sqrt{3}}{2 }=\frac{2( 3+ \sqrt{3})}{2}= 3+ \sqrt{3}[/tex]
