Решите уравнение: 4x^2-2x-5=0.

\[4x² - 2x - 5 = 0\]

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

\[= 4 + 80 = 84\]

\[x_{1} = \frac{2 + \sqrt{84}}{2 \cdot 4} = \frac{2 + 2\sqrt{21}}{8} =\]

\[= \frac{1 + \sqrt{21}}{4}\]

\[x_{2} = \frac{2 - \sqrt{84}}{2 \cdot 4} = \frac{2 - 2\sqrt{21}}{8} =\]

\[= \frac{1 - \sqrt{21}}{4}\]

\[Ответ:\ x = \frac{1 \pm \sqrt{21}}{4}.\]