Question

How do you solve `sqrt(58n) = 125(n + 4)`?

Answer 1

You need to square the both parts.
As `sqrt(58n)` is only defined for `n>0`, both parts of your equation are positive, so you can do so safely.

`sqrt(58n) = 125(n+4)`
`58n = 125^2(n+4)^2`
`58n = 125^2(n^2 + 8n + 16)`

Dividing both sides of the equation by `125^2` yields:
`58 / 125^2 n = n^2 + 8n + 16`
`<=>`
`n^2 + (8 - 58/125^2) n + 16 = 0`

This is a regular quadratic equation which can be solved by regular means. The numbers are really ugly though..