x² - x + 1 = 0

Use the quadratic formula:
                  ______ 
            -b ± Öb²-4ac
        x = —————————————
                2a 

where a = 1; b = -1; c = 1

                      _____________
             -(-1) ± Ö(-1)²-4(1)(1)
        x = ————————————————————————
                     2(1) 
                  ___ 
             1 ± Ö1-4
        x = ———————————
                 2

                  __ 
             1 ± Ö-3
        x = ———————————
                 2 

                   _ 
             1 ± iÖ3
        x = ——————————
                 2 

                   _ 
             1 ± iÖ3
        x = —————————
                 2 

                     _
             1     iÖ3
        x = ———— ± ——————
             2       2

                    _
             1     Ö3
        x = ——— ± ————i
             2      2

Using the +

x =  + 

Using the -

x =  - 

Edwin