28, x, √1078 is a Geometric Sequence. Find the common ratio(s)

3 Term Geometric Sequence With Variable Middle Term. Using the definition of common ratio leads to quadratic relation between the integer and irrational terms in the sequence. A fourth root irrational common ratio was determined.
NGO Hoai Diem Phuc wrote fascinating paper, March 2011, comparing quadratic irrationals that yields insight to the importance of continued fractions. Abstract mathematics at its finest, at least the parts I understood!!