Question

3+sqrt{z-6}=sqrt{z+9}

Answer 1

square both sides
\[9+6\sqrt{z-6}+z-6 = z+9\]
\[3+z+6\sqrt{z-6}=z+9\]
\[6\sqrt{z-6}=6\]
\[\sqrt{z-6}=1\]
Square both sides again
\[z-6=1\]
z=7