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The second term of a geometric sequence is equal to $\frac{10}{3} .$

The sum to infinity of the terms in the sequence is equal to $15.$

Find the two possible values for the common ratio of the sequence.

You are given that

u_{2} = \frac{10}{3}

and

S_{\infty} = 15

...

...so that

a r^{2} = \frac{10}{3}

and

\frac{a}{1 - r} = 15

Make $a$ the subject of the second equation and substitute it into the first.