$20a^2 - 5b^2 + 48ab =0$
$⇔ 20a^2 + 48ab - 5b^2 =0$
$⇔ 20a(a-\dfrac{1}{10}b)+50b(a-\dfrac{1}{10}b)=0$
$⇔ (a-\dfrac{1}{10}b)(20a+50b)=0$
$⇔$ \(\left[ \begin{array}{l}a-\dfrac{1}{10}b=0\\20a+50b=0\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}a-\dfrac{b}{10}=0\\20a+50b=0\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}a=\dfrac{b}{10}\\20×\dfrac{b}{10}+50b=0\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}a=\dfrac{b}{10}\\20×\dfrac{b}{10}+50b=0\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}a=\dfrac{b}{10}\\b=\dfrac{-5b}{2}\end{array} \right.\)
