To solve a quadratic equation [tex] ax^2+bx+c=0 [/tex] we can use the quadratic formula:
[tex] x_{1,2} = \cfrac{-b\pm\sqrt{b^2-4ac}}{2a} [/tex]
In your case, the equation is identified by [tex] a=c=1,\ b=-5 [/tex]
So, the solving formula yields
[tex] x_{1,2} = \cfrac{5\pm\sqrt{25-4}}{2} = \cfrac{5\pm\sqrt{21}}{2} [/tex]
So, the two solutions are derived by choosing the plus sign once, and the minus sign the other time:
[tex] x_{1} = \cfrac{5+\sqrt{21}}{2},\quad x_{2} = \cfrac{5-\sqrt{21}}{2} [/tex]
