Find the number of triples $$(x, a, b)$$ where $$x$$ is a real number and $$a, b$$ belong to the set $$\left\{1, 2, 3, 4, 5, 6, 7, 8, 9\right\}$$ such that $$x^{2}-a \left\{x\right\}+b=0$$, where $$\left\{x\right\}$$ denotes the fractional part of the real number $$x$$. (For example $$\left\{1.1\right\}$$ = 0.1 = $$\left\{−0.9\right\}$$.)