What is the solution for dealing with a taxi that was purchased through interest-bearing installments after discovering that the original agreement was usurious?

If the person did not genuinely purchase the car, then the amount they paid is a loan. This loan is either a goodly loan (qard hasan) to be repaid in like kind, or an usurious loan (qard ribawi) with an increase for the term, and an usurious loan is Islamically null and void.

Shaykh al-Islam Ibn Taymiyyah said: "Whenever the intention of the transactor is dirhams for dirhams with a term, then deeds are by intentions, and for every person is what they intended." He mentioned hadiths clarifying that "what two men agree upon, by which they intend dirhams for more dirhams with a term, is usury (riba)."

If you cannot annul the contract and return the money, and you have legally become the owner of half the car, then if you can repay the loan immediately, do so, and your share remains yours. If you cannot repay the loan immediately, and its owner is not content with recovering its like with the term outstanding, then it is permissible for you to transfer ownership to him from your share in the car or other assets equivalent to the money he paid, and you will not owe a debt.