# Solving equation using mathematica

How I can solve the equation :

$$R -\tan^{-1}[(m1/m3)*(k3/k1)] - \tan^{-1}[(m1/m2)*(k2/k1)]=0$$

I tried on it using findroot as following :

$$F = 0.56; w0 = 4*10^9*3.14; wp = 10*10^9*3.14; gama = 0.03*wp; T = 0.03*w0; e1 = -3.7; m1 = -1; e2 = 1; m2 = 1; e3 = -9.5; m3 = 1; w = 4.6*10^9*3.14; c = 3*10^8; k0 = w/c; k1 = Sqrt[(k0^2*e1*m1) - b^2]; k2 = Sqrt[b^2 - (k0^2*e2*m2)]; k3 = Sqrt[b^2 - (k0^2*e3*m3)]; R = 3.45; bbValue = FindRoot[R - ArcTan[(m1/m3)*(k3/k1)] - ArcTan[(m1/m2)*(k2/k1)] , {b,0.5}]$$


But it give me an error :

The line search decreased the step size to within tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find a sufficient decrease in the merit function. You may need more than MachinePrecision digits of working precision to meet these tolerances.

Regards

• How I can solve the equation Solve it for what? Feb 2 at 8:06
• @Ghoster i want to solve it for b Feb 2 at 8:08
• There’s no $b$ in your equation. What is the point of writing the equation you are solving but not giving all the necessary info to check whether your code is correct? Feb 2 at 8:11
• it is not an error, just a warning on accuracy of root found. b -> 2.34938*10^-13 - 3.75897 I} Feb 2 at 8:35
• @Ghoster there are b in k1 , k2 and k3 ... Feb 2 at 8:46

Plot[{Re[R - ArcTan[(m1/m3)*(k3/k1)] - ArcTan[(m1/m2)*(k2/k1)]], 