6. Решите уравнение: a) x2 – x = 0; B) 5x² + 8x – 4 = 0; д) 7x = 4x²; ж) 5х2 – 3 = 0;

1. a) $$x^2 - x = 0$$
   $$x(x - 1) = 0$$
   $$x_1 = 0, x_2 = 1$$
2. в) $$5x^2 + 8x - 4 = 0$$
   $$D = 8^2 - 4(5)(-4) = 64 + 80 = 144$$
   $$x = \frac{-8 \pm \sqrt{144}}{2(5)} = \frac{-8 \pm 12}{10}$$
   $$x_1 = \frac{-8 + 12}{10} = \frac{4}{10} = \frac{2}{5} = 0.4$$
   $$x_2 = \frac{-8 - 12}{10} = \frac{-20}{10} = -2$$
3. д) $$7x = 4x^2$$
   $$4x^2 - 7x = 0$$
   $$x(4x - 7) = 0$$
   $$x_1 = 0, x_2 = \frac{7}{4} = 1.75$$
4. ж) $$5x^2 - 3 = 0$$
   $$5x^2 = 3$$
   $$x^2 = \frac{3}{5}$$
   $$x = \pm \sqrt{\frac{3}{5}} = \pm \sqrt{\frac{15}{25}} = \pm \frac{\sqrt{15}}{5}$$

Ответ: a) x = 0, x = 1; B) x = 0.4, x = -2; д) x = 0, x = 1.75; ж) x = ±√15/5