Решите уравнение: x|x|+7x-6=0.

\[x|x| + 7x - 6 = 0\]

\[D = 7^{2} - 4 \cdot 1 \cdot ( - 6) =\]

\[= 49 + 24 = 73\]

\[x_{1} = \frac{- 7 + \sqrt{73}}{2}\]

\[x_{2} = \frac{- 7 - \sqrt{73}}{2}\ (не\ подходит).\]

\[D = 7^{2} - 4 \cdot ( - 1) \cdot ( - 6) =\]

\[= 49 - 24 = 25\]

\[x_{1} = \frac{- 7 + \sqrt{25}}{2 \cdot ( - 1)} = \frac{- 7 + 5}{- 2} =\]

\[= \frac{- 2}{- 2} = 1\ (не\ подходит)\]

\[x_{2} = \frac{- 7 - \sqrt{25}}{2 \cdot ( - 1)} = \frac{- 7 - 5}{- 2} =\]

\[= \frac{- 12}{- 2} = 6\ (не\ подходит)\]

\[Ответ:\ x = \frac{- 7 + \sqrt{73}}{2}.\]