How soon after did you take the second one?
Your urine for testing should have been in your bladder for at least 4 hours or it may not contain enough pregnancy hormone.
False positives are very uncommon, false negatives are very common.
If you took the second one right away I would doubt it's accuracy and also if you had drank a large quantity it may have been that your urine was too weak.
Either take another test but be sure to wait long enough before peeing, or make a doctors appt.