Have you tried using the formula ?
Note that there are no real solutions to this equation.
The question is not clear.. What does fixed point of an equation mean?Fixed points are defined for functions (as far as I know).
Also usually when one says "solve an equation", one should specify the domain... Is x real?
So assuming we want x real, is the question asking for the fixed point of the function f(x) = x^2 -(5/3)x +4/3 ?
You are asked to find fixed points of f(x) = x^2 -(5/3)x +4/3. Read this, to know the definition.
Now we know that a solution to f(x) = x is called a fixed point of f(x).
So find values of x for which f(x) = x.
f(x) = x implies x^2 -(5/3)x +4/3 = x, which implies x^2 -(8/3)x +4/3=0
Now hit it with the quadratic formula and get x. Do you get it now?