x² + 6x + 10 = 0

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

where a = 1; b = 6; c = 10

                     _____________
             -(6) ± Ö(6)²-4(1)(10)
        x = ————————————————————————
                     2(1) 
                   _____ 
             -6 ± Ö36-40
        x = —————————————
                  2

                   __ 
             -6 ± Ö-4
        x = ———————————
                 2 

                   ____ 
             -6 ± Ö-1·4
        x = ————————————
                 2 

                    _ 
             -6 ± iÖ4
        x = ———————————
                 2 

                      
             -6     2i
        x = ———— ± ————
              2      2
                  
        x = -3 ± i 
                       
Using the +, x = -3 + i 
Using the -, x = -3 - i

Edwin