$\left\{\begin{matrix}\\x=\frac{5-\sqrt{21}}{2}\approx 0.208712153\text{; }x=\frac{\sqrt{21}+5}{2}\approx 4.791287847\text{, }&\text{unconditionally}\\x=\frac{-\sqrt{-66+50\sqrt{3}i}-5\sqrt{3}i-5}{4}\approx -2.407654697-4.502832616i\text{, }&\frac{-\sqrt{-66+50\sqrt{3}i}-5\sqrt{3}i-5}{4}\neq 0\text{ and }-\frac{\sqrt{\frac{-33+25\sqrt{3}i}{2}}}{2}-\frac{5\sqrt{3}i}{4}-\frac{5}{4}\neq 0\\x=\frac{\sqrt{-66+50\sqrt{3}i}-5\sqrt{3}i-5}{4}\approx -0.092345303+0.172705597i\text{, }&\frac{\sqrt{-66+50\sqrt{3}i}-5\sqrt{3}i-5}{4}\neq 0\text{ and }\frac{\sqrt{\frac{-33+25\sqrt{3}i}{2}}}{2}-\frac{5\sqrt{3}i}{4}-\frac{5}{4}\neq 0\\x=\frac{-\sqrt{-50\sqrt{3}i-66}-5+5\sqrt{3}i}{4}\approx -0.092345303-0.172705597i\text{, }&\frac{-\sqrt{-50\sqrt{3}i-66}-5+5\sqrt{3}i}{4}\neq 0\text{ and }-\frac{\sqrt{\frac{-25\sqrt{3}i-33}{2}}}{2}+\frac{5\sqrt{3}i}{4}-\frac{5}{4}\neq 0\\x=\frac{\sqrt{-50\sqrt{3}i-66}-5+5\sqrt{3}i}{4}\approx -2.407654697+4.502832616i\text{, }&\frac{\sqrt{-50\sqrt{3}i-66}-5+5\sqrt{3}i}{4}\neq 0\text{ and }\frac{\sqrt{\frac{-25\sqrt{3}i-33}{2}}}{2}+\frac{5\sqrt{3}i}{4}-\frac{5}{4}\neq 0\end{matrix}\right.$

$x = \frac{\sqrt{21} + 5}{2} \approx 4.791287847$
$x=\frac{5-\sqrt{21}}{2}\approx 0.208712153$