# Solving equation in Mathematica

• Mathematica
Hello,

I have the following code to find the parameters Na and Q that make the expression equals $$10^{-10}$$:

Code:
Na =.;
Q =.;
MGF[s_, gC_] := 1/(1 - gC*s);
SNRdB = 0;
SNR = 10^(SNRdB/10);
gC = 0.5*SNR;
p = gA*gB;
A = 23;
Solve[((E^(A/2)*2^-Q)/SNR \!$$\*UnderoverscriptBox[\(\[Sum]$$, $$q = 0$$, $$Q$$]$$- \*SuperscriptBox[\(1$$, $$Na + q + 1$$]\)*Binomial[Q, q]*Re[
\*FractionBox[$$MGF[\(- \*FractionBox[\(A + \((2*Pi*I \((Na + q + 1)$$)\)\), $$2\ SNR$$]\),
gC]\),
FractionBox[$$A + 2*Pi*I \((Na + q + 1)$$\), $$2\ SNR$$]]]\)) ==
10^-10, {Na, Q}]
But it doesn't work? Anyone have any idea about how solving this equation?

## Answers and Replies

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Dale
Mentor
There are not analytical solutions for all equations. Functions like Solve, Reduce, DSolve, etc. will not always be able to find a solution. In such cases you can only find numerical solutions using e.g. FindRoot.

There are not analytical solutions for all equations. Functions like Solve, Reduce, DSolve, etc. will not always be able to find a solution. In such cases you can only find numerical solutions using e.g. FindRoot.
Thanks DaleSpam for replying,

So, you are saying that If I replace the "Solve" command by "FindRoot", I may get a result?

Regards

Dale
Mentor
The syntax for FindRoot is a little different than for Solve. You should use the help menu to find the new syntax and some examples.

The syntax for FindRoot is a little different than for Solve. You should use the help menu to find the new syntax and some examples.
Ok, I will. Thanks again