Problems in $\sqrt{5x+4}=x-2$ So when I solve $\sqrt{5x+4}=x-2$, I end up with $x(x-9)=0$. Yet only when $x=9$ is the original inequality satisfied. Can somebody give me some details on what exactly goes wrong here? 

At $x=0$, the LHS is $2$, while the RHS is $-2$. So the new solution come from squaring both sides, because $(2)^2=(-2)^2$.
