\[4x^{2} - 25 = 0\]
\[(2x - 5)(2x + 5) = 0\]
\[2x - 5 = 0\ \ \ \ \ \ \ \ 2x + 5 = 0\]
\[2x = 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2x = - 5\]
\[x = \frac{5}{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - \frac{5}{2}\]
\[x = 2,5\ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 2,5\]
\[Ответ:\ x = \pm 2,5.\]