[tex]a)\\\\2x^2-6x+3=0\\\\a=2,\ \ b=-6,\ \ c=3\\\\\Delta=b^2-4ac=(-6)^2-4*2*3=36-24=12\\\\\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=2\sqrt{3}\\\\x_{1}=\frac{-(-6)-2\sqrt{3}}{2*2}=\frac{6-2\sqrt{3}}{2*2}=\frac{\not{2}^1*(3-\sqrt{3})}{\not{2}^1*2}= \frac{3-\sqrt{3}}{2}\\\\x_{2}=\frac{-(-6)+2\sqrt{3}}{2*2}=\frac{6+2\sqrt{3}}{2*2}=\frac{\not{2}^1*(3+\sqrt{3})}{\not{2}^1*2}= \frac{3+\sqrt{3}}{2}[/tex]
[tex]b)\\\\ 6x^2=0\\\\x=0[/tex]
[tex]c)\\\\ x(x-2)=x^2+5\\\\x^2-2x=x^2+5\\\\x^2-x^2-2x=5\\\\-2x=5\ \ |:(-2)\\\\x=-\frac{5}{2}=-2\frac{1}{2}[/tex]
[tex]d)\\\\(x-2)^2-3(x-2)=2x^2-3-7x \\\\x^2-4x+4-3x+6-2x^2+3+7x =0\\\\13-x^2 =0\\\\(\sqrt{13}-x)(\sqrt{13}+x)=0\\\\\sqrt{13}-x=0\ \ lub\ \ \sqrt{13}+x=0\\\\x=\sqrt{13}\ \ lub\ \ x=-\sqrt{13}[/tex]
