\[x² - (5a + 7)x + 35a = 0\]
\[D = (5a + 7)^{2} - 4 \cdot 1 \cdot 35a =\]
\[= 25a^{2} + 70a + 49 - 140a =\]
\[= 25a^{2} - 70a + 49 = (5a - 7)^{2}\]
\[x_{1,2} = \frac{5a + 7 \pm \sqrt{(5a - 7)^{2}}}{2} =\]
\[= \frac{5a + 7 \pm |5a - 7|}{2}\]
\[1)\ a = 1,4:\]
\[x = \frac{5 \cdot 1,4 + 7 \pm |5 \cdot 1,4 - 7|}{2} =\]
\[= \frac{7 + 7 \pm 0}{2} = \frac{14}{2} = 7.\]
\[2)\ a > 1,4:\]
\[x_{1} = \frac{5a + 7 + 5a - 7}{2} =\]
\[= \frac{10a}{2} = 5a;\]
\[x_{2} = \frac{5a + 7 - 5a + 7}{2} = \frac{14}{2} = 7.\]
\[Ответ:\ \ a = 1,4 \Longrightarrow x = 7;\ \ \]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ a \neq 1,4 \Longrightarrow x_{1} = 5a;\ \ \]
\[x_{2} = 7.\]