Hydrogen has -1&+1 charge because in fact that every atom will be neutral but i assume that your asking for hydrogen ion charge that would be +1 as it loses one electron when it bonds with, say chlorine atom for example 
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In simple words u can say that it has both +1 and -1 charges because it can either give one electron or it can take one electron.. As first shell has  capacity of holding 2 electrons so by taking 1 it can be neutral and so by giving also... Hope u understood..

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