In[]:=
ClearAll["Global`*"]
In[]:=
(*n=10^(5);*)(*Concentration*)​​B=0.32;(*Magneticfield*)​​e=1.6*10^(-19);(*electriccharge*)​​e0=8.8*10^(-12);(*electricpermitivity*)​​m=0.91*10^(-30);(*electronmass*)​​M=1.67*10^(-27);(*protonmass*)​​
In[]:=
wpi[n_]:=Sqrt[(n*e^2)/(e0*M)];​​wpe[n_]:=Sqrt[(n*e^2)/(e0*m)];​​​​wci[B_]:=(e*B)/M;​​wce[B_]:=(e*B)/m;
In[]:=
(*wh-Upperhybridfrequency*)​​​​wh1[n_,B_]:=
1
2

2
wce[B]
+
2
wci[B]
+
2
wpe[n]
+
2
wpi[n]
+(-4wce[B]*wci[B]*(wce[B]*wci[B]+
2
wpe[n]
+
2
wpi[n]
)+
2
(
2
wce[B]
+
2
wci[B]
+
2
wpe[n]
+
2
wpi[n]
)
)​​wh[n_,B_]:=Sqrt[wce[B]^2+wpe[n]^2]​​​​Solve[{wh[n,B]==wh1[n,B]},n]
Out[]=
{{n-112595.-5.26393×
11
10
},{n-112595.+5.26393×
11
10
}}