Confusion in +v -v and ground in amplifier circuit
The word "ground" in an electrical circuit is always a relative term: in fact, it's the "reference" from which every other voltage is measured. *

So, if you have +24V, Gnd and -24V, that means that if you were to measure the voltage between -24V and +24V you would measure 48V. In fact, if you were to go through all of the documentation and add 24 to all of the voltages, you'd get exactly the same circuit, with 0V, 24V and 48V everywhere. That would make the novice happier - but confuse the professional no end! A usual audio signal rises and falls above and below some reference point (usually called "Ground"), so you'll get positive and negative voltages.

Your laptop power supply, that has 0V and 19V, fits inside the Gnd and +24V band. It doesn't work with the Gnd and -24V band at all. So you're going to need some kind of adapter or converter to get that to work.


  * Note that some circuits distinguish between "analog" ground and "digital" ground. That just means that analog signals reference against one ground, while digital signals reference against a different ground. The two grounds, if you measure the voltage between them, may not have any difference at all - but that's not guaranteed, and connecting the two may introduce interference, especially digital intereference on analog signals.