The present value of a 10-year annuity-immediate with level annual payments and interest rate i is x. The present value of a 20-year annuity-immediate with the same payment and interest rate is 1.5x. Find i.

So far I have:

where

So:

From here multiply both sides by i and get:

From here I'm not sure what to to do.

I know that

I was thinking that I could substitute and to setup and solve quadratic formula.

Doing so gives x=0.5,1

Therefore

But I'm not sure that's a proper way of solving the problem. Thanks