How this calculation works
Find real values that a linear fractional map sends to themselves.
THE FORMULA
x=(ax+b)/(cx+d) gives cx²+(d−a)x−b=0A worked example
(2x+3)/x fixes −1 and 3.
Good to know
This form requires a nonzero denominator slope and excludes the pole.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Find real values that a linear fractional map sends to themselves.
The primary result is labeled “Fixed points”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
This form requires a nonzero denominator slope and excludes the pole.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
(2x+3)/x fixes −1 and 3.
Which rule does this calculator apply?
x=(ax+b)/(cx+d) gives cx²+(d−a)x−b=0