$$x= a^{2} -4,(2x+1)( \sqrt{x+4} +1)=x+3 \Longrightarrow (2 a^{2} -7)(a+1)= a^{2} -1 \Longrightarrow (2 a^{2} -7)(a+1)=(a+1)(a-1) \Longrightarrow (a+1)(2 a^{2} -a-6)=0 \Longrightarrow a+1=0 \Longrightarrow a=-1,inadmissible \vee 2 a^{2} -a-6=0 \Longrightarrow a= -\frac{3}{2} ,inadmissible \vee a=2 \Longrightarrow x=0 \Longrightarrow S=[0]$$
