Note that there are no real solutions to this equation.
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 ?
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?