This does not look like a homework problem.
Beta=2;
c1=0.73;
c2=151;
c3=0.58;
c4=0.002;
c5=2.14;
c6=13.2;
c7=18.4;
c8=-0.02;
c9=-0.003;
k = @(x) 1./(x+c8.*Beta)-c9./(Beta.^3+1);
f = @(x) c1 * (c2*k(x) - c3*Beta - c4.*Beta.^c5 -c6).* exp( -c7*k(x)) - 0.45;
xv = fsolve(f, 1);
fprintf(1, 'x = %.10f\nk = %.10f\n\n', xv, k(xv))
x = 6.7434993463
k = 0.1495091516
