Hi, and thank you for your question!
Texas Instruments actually have a very good support system at their
website. They in fact have the entire 'guide book' for the TI-83 Plus
(in PDF form) on their website:
If you do not have 'Adobe Acrobat Reader', you will not be able to
read the 'guide book'. You can download this software at the
following website (it is a valuable program - PDF files are used
frequently around the internet):
The particular feature that you are looking for is described in
chapter 2 under
'Using the Equation Solver':
I have generated my own instructions from this guidebook (and have
also had some experience with similar calculators):
1. Start the 'Equation solver'. Do this by pressing [MATH]. You will
see a menu. Press  to select the "SOLVER".
(If an expression has already been placed in the EQN memory, it will
appear in the 'Interactive Equation Solver'. To remove this, use the
CURSOR UP KEY to move the cursor onto the LINE WITH THE EQUATION (the
top line). Then press CLEAR. You may now enter your own equation.)
2. Now, enter your own equation. You should at least read the first
chapter of the guide book to understand the basics about 'order of
operations' and generally the ways by which to enter an expression.
NOTE: The expression is assumed to be equal to zero, so some
algebraic juggling may have to take place - I will do that below.
3. Press ENTER. The 'Interactive Equation Solver' will be displayed.
It will show your variable as = 0 in the next line, and then show the
bounds of the search, which will be at a default value and do not need
to be changed.
4. Now press ALPHA then the button marked ENTER (but by pressing
ALPHA, you are activating the SOLVE function of this button - you will
see it above in green).
The value will be displayed after your variable.
I will now give you 3 examples, as you requested.
1. 3x + 7 = 28.
To begin, we must juggle the equation such that one side = 0.
Do this by deducting 28 from both sides of the equation.
Therefore, 3x - 21 = 0
Press [MATH]. Press .
(Note that 'X' need not be used as the variable when entering the
Press . Press ALPHA then MATH to use 'A' as a variable. Press
[-]. Then press  .
Press [ALPHA] [ENTER]
The correct value (7) should be displayed after the "A =" that has
appeared on the screen.
2. 5x - 20 = 100
Rearrange by deducting 100 from both sides -> 5x - 120 = 0
Press  [ALPHA] [MATH] [-]   .
Press [ALPHA] [Enter].
The correct value should appear after "A =" (24).
3. 17 - 2x = -1
Rearrange by adding 1 to both sides -> 18 - 2x = 0.
Press   [-]  [ALPHA] [MATH].
Press [ALPHA] [Enter].
The correct value should appear after "A =" (9).
Having explained all this, I would HIGHLY recommend reading the guide
book; at least the first few chapters. Note that there is another way
to find the result you are looking for - but it involved plotting a
graph and then using graph functions which you did not seem to want in
I hope this works for you! If you need any clarification, or these
instructions do not seem to work, please do not hesitate to ask.
Good luck with your calculator.