feel free to solve the problem too to get some context but I was intrigued by a part of it

This is the problem
>A faucet A takes 2 hours more than a faucet B to fill the same container. First they're opened at the same time for 1.5 hours. After that, faucet B is closed and then faucet A finishes filling the container in 1 hour. How long would each faucet take to fill the tank separately?
Solving this problem (leads to what I want to ask, spaced to let you try it first)

Since A = B + 2 I will call B as x to simplify things

In A hours faucet A fills 100%, so in 1 hour it fills 1/(x + 2)
In B hours faucet B fills 100%, so in 1 hour it fills 1/x

In 1 hour, faucets A and B fill 1/x + 1/(x+2)

In 1.5 hours both faucets fill 3(x+1)/(x(x+2))

In 2.5 hours the entire thing is filled, which gives the equation 3(x+1)/(x(x+2)) + 1/(x + 2) = 100%

Which leads to this equation x^2 - 2x + 3 = 0

My question is

What does the solution x = -1 mean? It solves the quadratic equation but if you substitute it in the other equations it gives nonsensical results (like in 2.5 hours 0 of the container is filled, while in 1 hour the container is filled and emptied simultaneously?). Why does -1 solve the equation but gives the result that faucet A fills the entire thing in 1 hour and faucet B empties the entire container in 1 hour?