Find the answer in this algebra

First let's $a=\sqrt{1+\sqrt{1+\sqrt{1+...}}}$ .Next $a=\sqrt{1+a}$ .After that $a^2=1+a$ .Only $\frac{1+\sqrt{5}}{2}$ or $\frac{1-\sqrt{5}}{2}$ solve the solution $a^2=1+a$ .But there no negative sign.So $a=\frac{1+\sqrt{5}}{2} \approx 1.6180339887498$