"The author leaves Laputa; is conveyed to Balnibarbi; arrives at the metropolis. A description of the metropolis, and the country adjoining. The author hospitably received by a great lord. His conversation with that lord."
Gulliver feels disrespected, because no one wants to talk about anything but math or music, and he can't compete with the Laputians in either field.
Also, he has become totally sick of the Laputians themselves and their dull conversation.
There is a lord in Laputa who has done many great things for the state, but he gets no respect, because he has no ear for music and no talent for math.
He and Gulliver bond, because they can talk sensibly to each other.
Gulliver asks this lord (Lord Munodi) to request to the King that Gulliver be let down in Lagado, the capital city.
The King agrees, and sends him down to the continent of Balnibarbi with Lord Munodi and some money.
Gulliver is relieved to be on firm ground again.
He is disappointed at the sight of Lagado, though: all of the people working there look hungry and unhappy.
Gulliver expresses his opinions of the poverty of Lagado to Lord Munodi, who suggests that they keep this conversation for a later time, when they are safely at Lord Munodi's own estates.
Lord Munodi's estates are beautiful, well-cultivated, and seem prosperous – totally the opposite of the other Balnibarbi lands.
Lord Munodi tells Gulliver that his estates (which look so great to Gulliver) bring frequent criticisms from other Laputians for mismanagement – he has left his orchards, fields, and home in the old model of his forefathers, while the rest of Balnibarbi has gone over to new ideas of farming.
The problem is, about 40 years before, some people from Balnibarbi went up to Laputa and came back filled with ideas for reform of everything – arts, science, all of it.
These guys found an academy in Lagado, filled with professors who promise all kinds of miracles – auto-ripening fruit, reduction of working hours, etc., etc.
Their plans have become total fads in all of the cities in the kingdom, but the problem is – all their calculations don't actually work.
So, these impractical men (Swift calls them "Projectors" (3.4.15)) have completely ruined the buildings and farmland of Balnibarbi with their farfetched ideas and equations.
Lord Munodi promises to get Gulliver an invitation to Lagado's Royal Academy if he wants it, which Gulliver does.