Let's determine the geometric mean of the following two expressions:

$$
\frac{2\left(a^{2}-a b\right)}{35 b}, \quad \frac{10 a}{7\left(a b-b^{2}\right)}
$$
The searched geometric mean ratio:

$$
\sqrt{\frac{2\left(a^{2}-a b\right)}{35 b} \cdot \frac{10 a}{7\left(a b-b^{2}\right)}}=\sqrt{\frac{4 a^{2}}{49 b^{2}}}=\frac{2 a}{7 b}
$$

Number of solutions: 30.