First mistake is to think there is any difference between what you describe as "positive voltage" and "negative voltage".
There is only voltage.
The concept of positive or negative relates to the potential of one point in relation to a reference point.
If you take the negative terminal of a battery as your reference point, then the voltage you measure at the positive terminal will be positive. Likewise, if you take the positive terminal of a battery as your reference point, then the voltage you measure at the negative terminal will be negative.
Same battery. Same voltage. It's how you measure it that makes the difference.