647. Найдите корень: a) 3x(2x - 1) - 6x = 30; б) 1,5x(3 + 2x) - 3x(x - 7) = -4x(15x-11); в) 5x(12x - 7) = 30 + 29x; г) 24x - 6x(13x - 9) = -13 - 13x(6x - 1).

a) \(3x(2x - 1) - 6x = 30\) \(6x^2 - 3x - 6x = 30\) \(6x^2 - 9x = 30\) Разделим обе части на 3: \(2x^2 - 3x = 10\) \(2x^2 - 3x - 10 = 0\) Решим квадратное уравнение через дискриминант: \(D = b^2 - 4ac = (-3)^2 - 4 * 2 * (-10) = 9 + 80 = 89\) \(x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{3 + \sqrt{89}}{4}\) \(x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{3 - \sqrt{89}}{4}\) Ответ: \(x_1 = \frac{3 + \sqrt{89}}{4}\), \(x_2 = \frac{3 - \sqrt{89}}{4}\) б) \(1.5x(3 + 2x) - 3x(x - 7) = -4x(15x-11)\) \(4.5x + 3x^2 - 3x^2 + 21x = -60x^2 + 44x\) \(25.5x = -60x^2 + 44x\) \(60x^2 - 18.5x = 0\) \(x(60x-18.5)=0\) \(x_1 = 0\) \(60x - 18.5=0\) \(x_2 = \frac{18.5}{60}\) = \(\frac{37}{120}\) Ответ: \(x_1 = 0, x_2 = \frac{37}{120}\) в) \(5x(12x - 7) = 30 + 29x\) \(60x^2 - 35x = 30 + 29x\) \(60x^2 - 64x - 30 = 0\) Разделим на 2: \(30x^2 - 32x - 15 = 0\) \(D = (-32)^2 - 4*30*(-15) = 1024 + 1800 = 2824\) \(x_1 = \frac{32 + \sqrt{2824}}{60} = \frac{32 + 2\sqrt{706}}{60} = \frac{16 + \sqrt{706}}{30}\) \(x_2 = \frac{32 - \sqrt{2824}}{60} = \frac{32 - 2\sqrt{706}}{60} = \frac{16 - \sqrt{706}}{30}\) Ответ: \(x_1 = \frac{16 + \sqrt{706}}{30}\), \(x_2 = \frac{16 - \sqrt{706}}{30}\) г) \(24x - 6x(13x - 9) = -13 - 13x(6x - 1)\) \(24x - 78x^2 + 54x = -13 - 78x^2 + 13x\) \(78x - 78x^2 = -13 - 78x^2 + 13x\) \(78x - 13x = -13\) \(65x = -13\) \(x = -\frac{13}{65}\) \(x = -\frac{1}{5}\) Ответ: \(x = -\frac{1}{5}\)