2. Solve the equation $\sqrt{8 x+5}+2\{x\}=2 x+2$. Here $\{x\}$ is the fractional part of the number $\mathrm{x}$, i.e., $\{x\}=x-[x]$. In the answer, write the sum of all solutions.
Solution. The equation is equivalent to the following $\sqrt{8 x+5}-2[x]-2=0, \quad[x]=n \in \mathbb{N}$, $n \leq x<n+1,2 n+2=\sqrt{8 x+5}$, for $n \geq-1$ we have $4 n^{2}+8 n-1=8 x$. Substituting into the double inequality

$$
8 n \leq 4 n^{2}+8 n-1<8 n+8, \quad 1 \leq 4 n^{2}<9, \quad \text { we get } \quad n=1 \quad \text { and } \quad n=-1 .
$$

Therefore,

$$
x=-\frac{5}{8} \quad x=\frac{11}{8}
$$

Answer: 0.75 .