$(2x + 7)^{2} = 9(x + 2)^{2}$
$\Leftrightarrow 4x^{2} + 28x + 49 = 9(x^{2} + 4x + 4)$
$\Leftrightarrow 4x^{2} + 28x + 49 = 9x^{2} + 36x + 36$
$\Leftrightarrow 5x^{2} + 8x - 13 = 0$
$\Leftrightarrow (5x + 13)(x - 1) = 0$
$\Leftrightarrow \left[ \begin{array}{l}5x + 13 = 0\\x - 1 = 0\end{array} \right.$
$\Leftrightarrow \left[ \begin{array}{l}x = -\dfrac{13}{5}\\x = 1\end{array} \right.$
