Найдите корни уравнения: (-x-1)(x-4)=x(4x-11).

Ответ:

\[( - x - 1)(x - 4) = x(4x - 11)\]

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

\[- x^{2} + 3x + 4 - 4x^{2} + 11x = 0\]

\[- 5x^{2} + 14x + 4 = 0\ \ \ \ | \cdot ( - 1)\]

\[5x^{2} - 14x - 4 = 0\]

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

\[= 196 - 4 \cdot 5 \cdot ( - 4) =\]

\[= 196 + 80 = 276\]

\[x_{1} = \frac{14 + 2\sqrt{69}}{10} = \frac{7}{5} + \frac{\sqrt{69}}{5}\]

\[x_{2} = \frac{14 - 2\sqrt{69}}{10} = \frac{7}{5} - \frac{\sqrt{69}}{5}\]

\[Ответ:x = \frac{7}{5} + \frac{\sqrt{69}}{5}\ \ \ и\ \ \ \]

\[x = \frac{7}{5} - \frac{\sqrt{69}}{5}.\]