Answer: Hello mate!
IF you have an quadratic equation of the form:
[tex]ax^{2} + bx + c= 0[/tex]
you can find the two solutions using:
[tex]x1 = \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]
and
[tex]x2 = \frac{-b - \sqrt{b^{2} - 4ac } }{2a}[/tex]
Now our equation is [tex]x^{2} - 3x + 1 = 0[/tex]
so a= 1, b = -3 and c = 1
now we just could replace it on the equations for x1 and x2:
[tex]x1 = \frac{3 + \sqrt{3^{2} - 4*1*1 } }{2*1} = \frac{3 + \sqrt{5} }{2}[/tex]
and similar for x2;
[tex]x2 = \frac{3 - \sqrt{5} }{2}[/tex]
