Sorcerer increasing casting time with metamagic

[Hama]

Where can I find that rule in the core book?

[MC Templar]

Under Feats: Metamagic Feats on SRD

Sorcerers and Bards: Sorcerers and bards choose spells as they cast them. They can choose when they cast their spells whether to apply their metamagic feats to improve them. As with other spellcasters, the improved spell uses up a higher-level spell slot. Because the sorcerer or bard has not prepared the spell in a metamagic form in advance, he must apply the metamagic feat on the spot. Therefore, such a character must also take more time to cast a metamagic spell (one enhanced by a metamagic feat) than he does to cast a regular spell. If the spell's normal casting time is a standard action, casting a metamagic version is a full-round action for a sorcerer or bard. (This isn't the same as a 1-round casting time.) The only exception is for spells modified by the Quicken Spell metamagic feat, which can be cast as normal using the feat.

For a spell with a longer casting time, it takes an extra full-round action to cast the spell.

[DesolateHarmony]

PRD link for metamagic feats

Edit: It is on p. 113 in the CRB.

[Xaratherus]

Indirectly related: Unless otherwise stated, prepared casters who have some limited spontaneous casting ability (like Clerics with heal spells, or Druids with summon creature spells) follow the same rules.