in the TMT, You have two parallel lines. One line is 2x the length of the other. If you have a quadratic and have to solve it, is it possible that you can have two numbers that work? So is it possible to have to answers of side lengths?
The triangle mid-segment theorem states that the mid-segment is 1/2AC, where AC is the length of the side parallel to the mid-segment. If there is a quadratic equation, there may be two solutions to this equation, the equation only. But when you plug these different solutions into the quadratic equation, the end result will remain the same, in this case the length of one of the sides.
So technically, there can be two solutions to the quadratic equation in some cases, but there is only one possible side length.