Найдите корни уравнения: (3x^2+x)/4-(2-7x)/5=(3x^2+17)/10.

Ответ:

\[5 \cdot \left( 3x^{2} + x \right) - 4 \cdot (2 - 7x) =\]

\[= 2 \cdot \left( 3x^{2} + 17 \right)\]

\[15x^{2} + 5x - 8 + 28x =\]

\[= 6x^{2} + 34\]

\[9x² + 33x - 42 = 0\ \ \ \ |\ :3\]

\[3x^{2} + 11x - 14 = 0\]

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

\[= 121 - 4 \cdot 3 \cdot ( - 14) =\]

\[= 121 + 168 = 289\]

\[x_{1} = \frac{- 11 + 17}{6} = \frac{6}{6} = 1\]

\[x_{2} = \frac{- 11 - 17}{6} = - \frac{28}{6} =\]

\[= - \frac{14}{3} = - 4\frac{2}{3}\]

\[Ответ:x = 1\ \ и\ \ \ x = - 4\frac{2}{3}.\]