Решите уравнение: (3x+2)(x-4)=5.

\[(3x + 2)(x - 4) = 5\]

\[3x² - 12x + 2x - 8 - 5 = 0\]

\[3x^{2} - 10x - 13 = 0\]

\[D = ( - 10)^{2} - 4 \cdot 3 \cdot ( - 13) =\]

\[= 100 + 156 = 256\]

\[x_{1} = \frac{10 + \sqrt{256}}{2 \cdot 3} = \frac{10 + 16}{6} =\]

\[= \frac{26}{6} = \frac{13}{3} = 4\frac{1}{3}\]

\[x_{2} = \frac{10 - \sqrt{256}}{2 \cdot 3} = \frac{10 - 16}{6} =\]

\[= - \frac{6}{6} = - 1\]

\[Ответ:x = 4\frac{1}{3};\ x = - 1.\]