Решите уравнение: (4x+2)/(1+2x)=x-6.

\[\frac{4x + 2}{1 + 2x} = x - 6\]

\[ОДЗ:\ \ 1 + 2x \neq 0\]

\(\ \ \ \ \ \Longrightarrow x \neq - 0,5\)

\[4x + 2 = (x - 6)(1 + 2x)\]

\[4x + 2 = x + 2x² - 6 - 12x\]

\[2x^{2} - 11x - 4x - 6 - 2 = 0\]

\[2x^{2} - 15x - 8 = 0\]

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

\[= 225 - 4 \cdot 2 \cdot ( - 8) =\]

\[= 225 + 64 = 289\]

\[x_{1} = \frac{15 + 17}{4} = \frac{32}{4} = 8\]

\[x_{2} = \frac{15 - 17}{4} = - \frac{2}{4} =\]

\[= - 0,5\ (не\ подходит\ по\ ОДЗ)\]

\[Ответ:x = 8.\]