Problem with 2nd order polynomial

[Liamtoh Resu]

I have been trying to understand this thread.

How can the estimates for x be obtained without running proot first?

There are significant differences of values for 'c' in the two images b C.Ret.
Why are there differences between the two solve answers.

What are the answers to the questions that C.Ret posed?

I hhave limited experiences with the type of problem that ktomb asked on the prime.

Thanks.