[tex]\frac{3x+2}{3x-2}=4-x \ \ /\cdot(3x-2)\\\\\\Dziedzina:\\3x-2\neq 0\\3x\neq 2\\x\neq \frac{2}{3}\\D = R \setminus\{\frac{2}{3}\}\\\\\\3x+2 = (4-x)(3x-2)\\\\3x+2 = 12x-8-3x^{2}+2x\\\\3x+2 = -3x^{2}+14x-8\\\\3x^{2}+3x-14x+2+8 = 0\\\\3x^{2}-11x+8 = 0\\\\a = 3, \ b = -11, \ c = 10\\\\\Delta = b^{2}-4ac = (-11)^{2}-4\cdot3\cdot10 = 121-120 = 1\\\\\sqrt{\Delta} = \sqrt{1} = 1[/tex]
[tex]x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-(-11)-1}{2\cdot3} =\frac{10}{6} = \frac{5}{3} = 1\frac{2}{3}\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-(-11)+1}{6} = \frac{12}{6} = 2[/tex]
