Fitting Nonlinear Data to a Linear Equation: Manual Calculation Process

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Doctor_Doom
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Hey guys I'm completing an experiment and I'm required to extrapolate data by performing nonlinear curve fitting.

I have 3 sets of data: (x1, y1); (x2, y2); (x3, y3).

I'm required to fit the above mentioned sets of data to the following equation :

[PLAIN]http://img245.imageshack.us/img245/8121/37594905.png

In order to gain maximum marks manual operations would be required. Thus I would prefer if someone could provide me with an initial hint on how to start a manual calculation process.

I'm assuming that performing the calculations manually for the curve fitting would not be a huge task due to the fact that there are only 3 sets of data points.

So I'm hoping someone could provide me with the starting hint on how to perform the manual (NO SOFTWARE USED) calculations for the curve fitting of the above equation.
 
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Just plug in your data pairs for x and y, and solve the linear system of this three equations for A, B, C.

ehild
 
Additionally, the problem isn't nonlinear. The equation is linear in the unknowns A, B, C as implied in ehild's reply. It is nonlinear in x, but the x's are known.