Решите уравнение: x|x|+5x-4=0.

\[x|x| + 5x - 4 = 0\]

\[D = 5^{2} - 4 \cdot 1 \cdot ( - 4) =\]

\[= 25 + 16 = 41\]

\[x_{1} = \frac{- 5 + \sqrt{41}}{2}\]

\[x_{2} = \frac{- 5 - \sqrt{41}}{2}\ (не\ подходит).\]

\[D = 5^{2} - 4 \cdot ( - 1) \cdot ( - 4) =\]

\[= 25 - 16 = 9\]

\[x_{1} = \frac{- 5 + \sqrt{9}}{2 \cdot ( - 1)} = \frac{- 5 + 3}{- 2} =\]

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

\[x_{2} = \frac{- 5 - \sqrt{9}}{2 \cdot ( - 1)} = \frac{- 5 - 3}{- 2} =\]

\[= \frac{- 8}{- 2} = 4\ (не\ подходит)\]

\[Ответ:\ x = \frac{- 5 + \sqrt{41}}{2}.\]