Найдите корни уравнения: 5·(x-2)=(3x+2)(x-2).

Ответ:

\[5 \cdot (x - 2) = (3x + 2)(x - 2)\]

\[5x - 10 = 3x^{2} - 6x + 2x - 4\]

\[3x^{2} - 4x - 4 - 5x + 10 = 0\]

\[3x² - 9x + 6 = 0\ \ \ \ |\ :3\]

\[x^{2} - 3x + 2 = 0\]

\[D = b^{2} - 4ac = 9 - 4 \cdot 1 \cdot 2 =\]

\[= 9 - 8 = 1\]

\[x_{1} = \frac{3 + 1}{2} = \frac{4}{2} = 2\]

\[x_{2} = \frac{3 - 1}{2} = \frac{2}{2} = 1\]

\[Ответ:x = 2\ \ и\ \ \ x = 1.\]