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In general a small increase in voltage is perfectly safe for most common items. Generally the only thing that changes with a small increase in voltage is a similar small decrease in the current required to achieve the same desired result.
Even elctronic dvices which require a stable voltage generally have a voltage regulator built in to stabilise the voltage and protect from voltage spikes which happen every time a switch is switched.
This being the case electronics will be the most sensitive and more care should be taken but an increase from 12V to 13.8 shouldn't be of any concern. A fully charged 12V battery measures somewhat higher than 12 volts and as it is discharged it falls below the 12 V mark.
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