$$x=2+\sqrt{5}:x^{2}+\frac{1}{x}$$
$x=\frac{2^{\frac{2}{3}}\sqrt[3]{3\sqrt{204\sqrt{5}+381}+27\sqrt{5}+34}}{6}+\frac{2^{\frac{2}{3}}\sqrt[3]{-3\sqrt{204\sqrt{5}+381}+27\sqrt{5}+34}}{6}+\frac{2}{3}\approx 2.68325342$
