\(2a=3b\Rightarrow\dfrac{a}{3}=\dfrac{b}{2}\Rightarrow\dfrac{3a}{9}=\dfrac{7b}{14}\Rightarrow\dfrac{3a}{63}=\dfrac{7b}{98}\left(1\right)\)

\(5b=7c\Rightarrow\dfrac{b}{7}=\dfrac{c}{5}\Rightarrow\dfrac{7b}{49}=\dfrac{5c}{25}\Rightarrow\dfrac{7b}{98}=\dfrac{5c}{50}\left(2\right)\)

Từ (1)(2) \(\Rightarrow\dfrac{3a}{63}=\dfrac{7b}{98}=\dfrac{5c}{50}\)

Áp dụng tính chất của dãy tỉ số bằng nhau ,ta có :

\(\dfrac{3a}{63}=\dfrac{7b}{98}=\dfrac{5c}{50}=\dfrac{3a+5c-7b}{63+50-98}=\dfrac{30}{15}=2\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{3a}{63}=2\Rightarrow3a=126\Rightarrow a=42\\\dfrac{7b}{98}=2\Rightarrow7b=196\Rightarrow b=28\\\dfrac{5c}{50}=2\Rightarrow5c=100\Rightarrow c=20\end{matrix}\right.\)

Vậy \(a=42;b=28;c=20\)