Notice that the formula in the question actually gives the distance between two points in the plane.
d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Let's put the question in context using an example.
If the distance between points A(6,y_1) and B(2,1) is 5 units, what is y_1?
We can use our solution with (x_2,y_2)=(2,1), x_1=6, and d=5 to get the answer.
A point with an x-coordinate at 6, which is 5 away from B(2,1), is A(6,-2).
However, if we look at the diagram below, we can see that point C(6,4) is also 5 units away from B.
The second coordinate y_1=4 is also a solution to the starting equation.
Let's investigate our solution to see the moment at which we missed this second solution.
The problematic part is where we take the square root of both sides.
d^2-(x_2-x_1)^2=(y_2-y_1)^2
If the square of a number is given, then the number itself can be positive or negative.
We only considered the positive solution.
Let's now work out the other possible solution.
