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? 

When you square both sides to solve, you create an extra incorrect answer. See, at x=0, the squares of both sides of the equation are equal, but the sides of the original equation are not. The constraint that x-2 cannot be negative is lost in the process of squaring, and thus an extra solution is created. 
