$\sqrt[]{4x-12}$ - $\sqrt[]{x-3}$ = $\sqrt[]{2x+1}$
⇔$\sqrt[]{4.(x-3)}$ - $\sqrt[]{x-3}$ = $\sqrt[]{2x+1}$
⇔2$\sqrt[]{x-3}$ - $\sqrt[]{x-3}$ = $\sqrt[]{2x+1}$
⇔$\sqrt[]{x-3}$ = $\sqrt[]{2x+1}$
⇔$(\sqrt[]{x-3})^{2}$ =$(\sqrt[]{2x+1})^{2}$
⇔x-3=2x+1
⇔-x=4
⇔x=-4