Are these equally used in Spain, or is the first option more common?
- ¿Se puede pagar con tarjeta?
- ¿Es posible pagar con tarjeta?
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The difference is minimal.
¿Se puede pagar con tarjeta? is slightly more colloquial, and one might use it more often to ask friends if a particular place accepts card payments.
When asking the waiter/seller directly, one might more often say ¿Es posible pagar con tarjeta? or ¿Puedo pagar con tarjeta?. In any case, in Spain, interaction with waiters or sellers is usually colloquial enough that it will not make much of a difference.