[tex]\sqrt{x+4}-2 = x \Rightarrow \sqrt{x+4} = x+2[/tex]
[tex]\\\text{DVA:}[/tex]
[tex]x+4\geq 0 \,\wedge \,x+2\geq 0 \Rightarrow x\geq -4 \, \wedge\, x\geq -2 \Rightarrow[/tex]
[tex]\Rightarrow x\in [-2,+\infty)[/tex]
[tex]\\\sqrt{x+4} = x+2\Big|^2 \Rightarrow x+4 = (x+2)^2\Rightarrow[/tex]
[tex]\Rightarrow x+4 = x^2+4x+4 \Rightarrow x^2+2x+x = 0 \Rightarrow[/tex]
[tex]\Rightarrow x^2+3x = 0 \Rightarrow x(x+3) = 0\Rightarrow[/tex]
[tex]\Rightarrow S= \{-3;0\} \cap [-2,+\infty) \Rightarrow \boxed{S = \{0\}}[/tex]
