Решите уравнение: 4x^3+x^2-x+5=0.

\[4x^{3} + x^{2} - x + 5 = 0\]

\[5x^{3} + 5 - x^{3} + x^{2} - x = 0\]

\[5\left( x^{3} + 1 \right) - \left( x^{3} - x^{2} + x \right) = 0\]

\[5(x + 1)\left( x^{2} - x + 1 \right) - x\left( x^{2} - x + 1 \right) = 0\]

\[\left( x^{2} - x + 1 \right)(5x + 5 - x) = 0\]

\[\left( x^{2} - x + 1 \right)(4x + 5) = 0\]

\[1)\ 4x + 5 = 0\]

\[4x = - 5\]

\[x = - \frac{5}{4} = - 1,25.\]

\[2)\ x^{2} - x + 1 = 0\]

\[D = 1 - 4 = - 3 < 0\]

\[нет\ корней.\]

\[Ответ:x = - 1,25.\]