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Verified answer
[tex]x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-5\right)}}{2\cdot \:1}\\x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{21}}{2\cdot \:1}\\\\x_1=\frac{-\left(-1\right)+\sqrt{21}}{2\cdot \:1},\:x_2=\frac{-\left(-1\right)-\sqrt{21}}{2\cdot \:1}\\\\x=\frac{1+\sqrt{21}}{2},\:x=\frac{1-\sqrt{21}}{2}[/tex]