Найдите область определения функции y=5/(корень из (5-14x-3x^2)).

\[y = \frac{5}{\sqrt{5 - 14x - 3x^{2}}}\]

\[5 - 14x - 3x^{2} > 0\]

\[3x^{2} + 14x - 5 < 0\]

\[D = 49 + 15 = 64\]

\[x_{1} = \frac{- 7 + 8}{3} = \frac{1}{3};\ \ x_{2} = \frac{- 7 - 8}{3} = - 5\]

\[3(x + 5)\left( x - \frac{1}{3} \right) < 0\]

\[D(y) = \left( - 5;\frac{1}{3} \right).\]