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how do nodes agree or disagree after new block is create?

I am new to blockchain discipline and I learn one article.
article

On this article of Authorization chapter, it’s mentioned that “For a public blockchain, the choice so as to add a transaction to the chain is made by consensus. Which means that the vast majority of “nodes” (or computer systems within the community) should agree that the transaction is legitimate.”

However, I am unable to think about the settlement scenario by nodes.

How do all nodes agree on that new block  ought to be added to blockchain ? Do nodes should agree or disagree manually like by clicking a “Agree!!” or “Disagree!!” button?

Additionally, does not it take soooooo very long time? I imply that there are tons nodes within the community and to collect all nodes settlement, it’s going to be sooooo very long time I suppose.

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