Find two consecutive positive integers whose product is 380

The answer is 19 and 20.
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Let A = the smaller integer.

(A) * (A + 1) = 380
Then A^2 + A = 380
And then A^2 + A - 380 = 0

Quadratic formula gives:

A = [-1 + SqRt(1 + 1520)] / 2 -OR- A = [-1 - SqRt(1 + 1520)] / 2
Then A = [-1 + SqRt(1521)] / 2 -OR- A = [-1 - SqRt(1521)] / 2
Then A = [-1 + 39] / 2 -OR- A = [-1 - 39] / 2
Then A = 38 / 2 -OR- A = -40 / 2
Finally A = 19 -OR- A = -20

Therefore the two consecutive integers are 19 and 20 OR -20 and -19; but the requiremet calls for positive integers. Therefore the answer is 19 and 20.
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The asker gets the answer served on a gold plate and did no work. Only a small percent of the askers would actually read and learn the full workings, while the other big majority will never read the workings, take the answer and stay in the darkness for such questions.

The usual way around is to help the asker find the answer himself/herself by providing good "hints" which will make him/her think and understand in the right direction.