a)
[tex]2x^{2} - 6x = 0 \ \ /:2\\\\x^{2}-3x = 0\\\\x(x - 3) = 0\\\\x = 0 \ \vee \ x-3 = 0\\\\x = 0 \ \vee \ x = 3\\\\x \in \{0,3\}[/tex]
b)
[tex]\frac{3}{4}x^{2}-\frac{5}{12} \ x = 0 \ \ /\cdot12\\\\9x^{2}-5x = 0\\\\x(9x-5) = 0\\\\x = 0 \ \vee \ 9x-5 =0\\\\x = 0 \ \vee \ 9x = 5 \ \ /:9\\\\x = 0 \ \vee \ x = \frac{5}{9}\\\\x \in \{0, \frac{5}{9}\}[/tex]
c)
[tex]3x + 4x^{2} = 0\\\\4x^{2}+3x = 0\\\\x(4x+3) = 0\\\\x = 0 \ \vee \ 4x+3 = 0\\\\x = 0 \ \vee \ 4x = -3 \ \ /:4\\\\x = 0 \ \vee \ x = -\frac{3}{4}\\\\x \in \{-\frac{3}{4}, 0\}[/tex]
d)
[tex]-\frac{2}{3}x - 6x^{2} = 0 \ \ /\cdot(-\frac{3}{2})\\\\9x^{2}+x = 0\\\\x(9x+1) = 0\\\\x = 0 \ \vee \ 9x+1 = 0\\\\x = 0 \ \vee \ 9x = -1 \ \ /:9\\\\x = 0 \ \vee \ x = -\frac{1}{9}\\\\x \in \{-\frac{1}{9}, 0\}[/tex]
e)
[tex]5x = 10x^{2} \ \ /:(-5)\\\\-x = -2x^{2}}\\\\2x^{2}-x = 0\\\\x(2x-1) = 0\\\\x = 0 \ \vee \ 2x-1 = 0\\\\x = 0 \ \vee \ 2x = 1 \ \ /:2\\\\x = 0 \ \vee \ x = \frac{1}{2}\\\\x \in\{0,\frac{1}{2}\}[/tex]
f)
[tex]\frac{1}{2}x^{2}-\frac{1}{4}x = \frac{2}{3}x^{2} \ \ /\cdot(-12)\\\\-6x^{2}+3x = -8x^{2}\\\\8x^{2}-6x^{2}+3x = 0\\\\2x^{2}+3x = 0\\\\x(2x+3) = 0\\\\x = 0 \ \vee \ 2x+3 = 0\\\\x = 0 \ \vee \ 2x = -3 \ \ /:2\\\\x = 0 \ \vee \ x = -1,5\\\\x \in \{-1,5; 0\}[/tex]
