Найдите корни уравнения: (2x^2+x)/5=(4x-2)/3.

Ответ:

\[\frac{2x^{2} + x}{5} = \frac{4x - 2}{3}\ \ \ \ \ \ \ | \cdot 15\]

\[3 \cdot \left( 2x^{2} + x \right) = 5 \cdot (4x - 2)\]

\[6x^{2} + 3x = 20x - 10\]

\[6x² - 17x + 10 = 0\]

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

\[= 289 - 4 \cdot 6 \cdot 10 =\]

\[= 289 - 240 = 49\]

\[x_{1} = \frac{17 + 7}{12} = \frac{24}{12} = 2\]

\[x_{2} = \frac{17 - 7}{12} = \frac{10}{12} = \frac{5}{6}\]

\[Ответ:x_{1} = 2;\ \ x_{2} = \frac{5}{6}.\]