If ax2 + bx + c = 0, then:
        -b + root( b2 - 4ac )
 x = ----------------------------
            2 a

Want to use this on your fancy TI-83? Use this program:
:a+bi
:Lbl 1
:ClrHome
:Input "A=",A
:Input "B=",B
:Input "C=",C
:If A=0:Goto 1
:(-B+root(B2-4AC))/(2A) -> X
:(-B-root(B2-4AC))/(2A) -> Y
:Disp "ANSWERS STORED"
:Disp "AS X AND Y"
:Disp X
:Disp Y
Where -> indicates the "store" operator, a+bi indicates the command that sets a+bi mode and root() indicates the square root operator.