# 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? Commented Feb 2, 2023 at 8:06
• @Ghoster i want to solve it for b Commented Feb 2, 2023 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? Commented Feb 2, 2023 at 8:11
• it is not an error, just a warning on accuracy of root found. b -> 2.34938*10^-13 - 3.75897 I} Commented Feb 2, 2023 at 8:35
• @Ghoster there are b in k1 , k2 and k3 ... Commented Feb 2, 2023 at 8:46

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