Решите уравнение: x+2=15/(4x+1)

Ответ:

\[x + 2 = \frac{15}{4x + 1}\]

\[ОДЗ:4x + 1 \neq 0;\]

\[4x \neq - 1\]

\[x \neq - \frac{1}{4} \neq - 0,25.\]

\[(x + 2)(4x + 1) = 15\]

\[4x^{2} + 8x + x + 2 - 15 = 0\]

\[4x^{2} + 9x - 13 = 0\]

\[D = 81 + 208 = 289 = 17^{2}\]

\[x_{1} = \frac{- 9 + 17}{8} = 1;\]

\[x_{2} = \frac{- 9 - 17}{8} = - \frac{26}{8} =\]

\[= - \frac{13}{4} = - 3\frac{1}{4} = - 3,25.\]

\[Ответ:x = - 3,25;x = 1.\]