[tex]a)\\\\2x^2-6x=0\\\\2x(x-3)=0\\\\2x=0\ \ \vee\ \ x-3=0\\\\x=0\ \ \vee\ \ x=3[/tex]
[tex]b)\\\\4x^2-5x=0\\\\ x(4x-5)=0\\\\ x=0\ \ \vee\ \ 4x-5=0\\\\x=0\ \ \vee\ \ 4x=5\ \ |:4\\\\x=0\ \ \vee\ \ x=\frac{5}{4}[/tex]
[tex]c)\\\\3x+4x^2 =0\\\\ x(3+4x )=0\\\\ x=0\ \ \vee\ \ 3+4x =0\\\\x=0\ \ \vee\ \ 4x=-3\ \ |:4\\\\x=0\ \ \vee\ \ x=-\frac{3}{4}[/tex]
[tex]d)\\\\ \frac{x^2}{2}=7x\ \ |*2\\\\x^2=14x\\\\x^2-14x=0\\\\x(x-14)=0\\\\x=0\ \ \vee\ \ x-14=0\\\\x=0\ \ \vee\ \ x=14[/tex]
[tex]e)\\\\ x=\sqrt{2}x^2\\\\\sqrt{2}x^2-x=0\\\\x(\sqrt{2}x-1)=0\\\\x=0\ \ \vee\ \ \sqrt{2}x-1=0\\\\ \sqrt{2}x=1\ \ |:\sqrt{2}\\\\x=\frac{1}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}[/tex]
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[tex]a)\\\\2x^2-6x=0\\\\2x(x-3)=0\\\\2x=0\ \ \vee\ \ x-3=0\\\\x=0\ \ \vee\ \ x=3[/tex]
[tex]b)\\\\4x^2-5x=0\\\\ x(4x-5)=0\\\\ x=0\ \ \vee\ \ 4x-5=0\\\\x=0\ \ \vee\ \ 4x=5\ \ |:4\\\\x=0\ \ \vee\ \ x=\frac{5}{4}[/tex]
[tex]c)\\\\3x+4x^2 =0\\\\ x(3+4x )=0\\\\ x=0\ \ \vee\ \ 3+4x =0\\\\x=0\ \ \vee\ \ 4x=-3\ \ |:4\\\\x=0\ \ \vee\ \ x=-\frac{3}{4}[/tex]
[tex]d)\\\\ \frac{x^2}{2}=7x\ \ |*2\\\\x^2=14x\\\\x^2-14x=0\\\\x(x-14)=0\\\\x=0\ \ \vee\ \ x-14=0\\\\x=0\ \ \vee\ \ x=14[/tex]
[tex]e)\\\\ x=\sqrt{2}x^2\\\\\sqrt{2}x^2-x=0\\\\x(\sqrt{2}x-1)=0\\\\x=0\ \ \vee\ \ \sqrt{2}x-1=0\\\\ \sqrt{2}x=1\ \ |:\sqrt{2}\\\\x=\frac{1}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}[/tex]