The quadratic formula is:
[tex]x= \frac{-b \pm \sqrt{b^2-4ac} }{2a} [/tex]
In your equation:
[tex]a=1[/tex]
[tex]b=-6[/tex]
[tex]c=4[/tex]
So now we just plug and chug:
[tex]x= \frac{-(-6) \pm \sqrt{(-6)^2-4(1)(4)} }{2(1)} [/tex]
[tex]x= \frac{6 \pm \sqrt{36-16} }{2} [/tex]
[tex]x= \frac{6 \pm \sqrt{20} }{2}[/tex]
[tex]x= \frac{6 \pm 2\sqrt{5} }{2}[/tex]
[tex]x= 3\pm \sqrt{5} }[/tex]
So the two solutions are [tex]x= 3 + \sqrt{5} }[/tex] and [tex]x= 3 - \sqrt{5} }[/tex]
