$5x^2-21x+20=0$
$⇔5(x^2-\frac{21}{5}x+4)=0$
$⇔5[(x^2-2.\frac{21}{10}x+\frac{441}{100})-\frac{41}{100}]=0$
$⇔5[(x-\frac{21}{10})^2-(\frac{\sqrt{41}}{10})^2]=0$
$⇔5(x-\frac{21}{10}+\frac{\sqrt{41}}{10})(x-\frac{21}{10}-\frac{\sqrt{41}}{10})=0$
$⇔5(x-\frac{21-\sqrt{41}}{10})(x-\frac{21+\sqrt{41}}{10})=0$
$⇔\left[ \begin{array}{l}x-\frac{21-\sqrt{41}}{10}=0\\x-\frac{21+\sqrt{41}}{10}=0\end{array} \right.⇔\left[ \begin{array}{l}x=\frac{21-\sqrt{41}}{10}\\x=\frac{21+\sqrt{41}}{10}\end{array} \right.$
Vậy $S=${$\frac{21-\sqrt{41}}{10};\frac{21+\sqrt{41}}{10}$}.