$(5x -4)² - (x -3)² = 0$
$⇔ (5x -4 -x +3).(5x -4 +x -3) = 0$
$⇔ (4x -1).(6x -7) = 0$
$⇔ \left[ \begin{array}{l}4x -1=0\\6x -7=0\end{array} \right. ⇔ \left[ \begin{array}{l}x=\frac{1}{4}\\x=\frac{7}{6}\end{array} \right.$
$Vậy$ $S =$ {$\frac{1}{4}; \frac{7}{6}$}