Решите уравнение: 3x^2-4x-5=0.

\[3x² - 4x - 5 = 0\ \ \]

\[a = 3,\ \ b = - 4,\ \ c = - 5\]

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

\[= ( - 4)^{2} - 4 \cdot 3 \cdot ( - 5) =\]

\[= 16 + 60 = 76\]

\[x_{1,2} = \frac{- b \pm \sqrt{D}}{2a}\]

\[x_{1} = \frac{- ( - 4) + \sqrt{76}\ }{2 \cdot 3} =\]

\[= \frac{4 + 2\sqrt{19}}{6} = \frac{2 + \sqrt{19}}{3\ }\]

\[x_{2} = \frac{- ( - 4) - \sqrt{76}\ }{2 \cdot 3} =\]

\[= \frac{4 - 2\sqrt{19}}{6} = \frac{2 - \sqrt{19}}{3\ }\]

\[Ответ:\ x = \frac{2 - \sqrt{19}}{3\ };\ \ \]

\[x = \frac{2 + \sqrt{19}}{3\ }.\]