[tex]\frac{6x-1}{3x-2}=3x+2 \ \ /\cdot(3x-2), \ \ \ \ \ Z: \ x \neq \frac{2}{3}\\\\(3x-2)(3x+2) = 6x-1\\\\9x^{2}-4=6x-1\\\\9x^{2}-6x-4+1 = 0\\\\9x^{2}-6x-3 = 0 \ \ /:3\\\\3x^{2}-2x-1 = 0\\\\\Delta = b^{2}-4ac = (-2)^{2}-4\cdot3\cdot(-1) = 4+12 = 16\\\\\sqrt{\Delta} = \sqrt{16} = 4\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} =\frac{2-4}{2\cdot3} = \frac{-2}{6} = -\frac{1}{3}[/tex]
[tex]x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{2+4}{6} = \frac{6}{6} = 1\\\\x \in\{-\frac{1}{3}, 1\}[/tex]
