finding variables in polynomial expressions

Hi, have an issue i cant solve with matlab, i wish to get matlab to solve this equation for k1 k2 and ke.

Have tried res = solve((a-b),[k1 k2 ke]) but does not give the results im looking for

clc
clear, close all;
syms s k1 k2 ke
A = [0 -83.33; 500 -10];
B = [166.67; 0];
C= [0 1];
K = [k1 k2];
 
A2 = [A-B*K B*ke; -C 0];

a = det(s*eye(3)-A2);
b = (s+1600)*(s^2+160*s+30790);

how i do it by hand

Answer 1

[Walter Roberson]

syms s k1 k2 ke
A = [0 -83.33; 500 -10];
B = [166.67; 0];
C= [0 1];
K = [k1 k2];
 
A2 = [A-B*K B*ke; -C 0];

a = det(s*eye(3)-A2);
b = (s+1600)*(s^2+160*s+30790);

eqn = collect(a-b,s)

eqn = 

sol = solve(coeffs(eqn, s))

sol = struct with fields:
    k1: 25000/2381
    k2: 45525/16667
    ke: 9852800/16667

[fredrik s]

Excellent, just what i was looking for. Thanks alot :D

Answer 2

[Torsten]

A = [0 -83.33; 500 -10];
B = [166.67; 0];
C = [0 1];
K = @(k1,k2)[k1 k2];

A2 = @(k1,k2,ke) [A-B*K(k1,k2) B*ke; -C 0];
a  = @(k1,k2,ke,s) det(s*eye(3)-A2(k1,k2,ke));
b  = @(s)(s+1600)*(s^2+160*s+30790);

fun = @(k1,k2,ke)[a(k1,k2,ke,-1)-b(-1);a(k1,k2,ke,0)-b(0);a(k1,k2,ke,1)-b(1)];
sol = fsolve(@(k)fun(k(1),k(2),k(3)),[0;0;0]);
k1 = sol(1)
k2 = sol(2)
ke = sol(3)

[fredrik s]

Thanks, works like a charm. Is it possible to solve with syms s k1 k2 ke, so the decleration @(k1,k2,ke)is avoided in order to easily expand to k1 k2 k3...kn