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For this you need to have a TI-82 or up calculator. I'm assuming most people will probably have the TI-83+ so I'm going to make the tut for that. If you have a different model the coding is probably either the same, or slightly different (for example I have a ti-89 titanium as well, and the coding is almost exactly the same).
1. Click the PRGM button.
2. Go to "New" and create a new program.
3. Name it "QUADEQ" or something to that effect.
4. There are a couple commands that you will need. To find the list of commands, click the PRGM button again. The "→" symbol is the store (STO→

command and can be found right above the ON button. The = sign can be found by pressing 2nd and then MATH.
5. Enter this code exactly:
:ClrHome
isp "FOR AX^2+BX+C=0:"
rompt A
rompt B
rompt C
:√(B^2-4*A*C)→
-B+D)/(2*A)→M
-B-D)/(2*A)→N
isp "SOLUTIONS:",M,N
:
6. Press 2nd MODE to quit.
7. Press PRGM and open the program you just made under the EXEC tab.
8. Now when you have a quadratic equation in standard form (ax^2+bx+c=0) just enter the values of a, b, and c.
9. Test it out to see if it works. Try a simple equation like x^2+2x+1=0 (so you would enter 1, 2, and 1 in the calculator). The answers for that one should be -1 and -1.