8(m-4)^4 - 10(m-4)^2 + 3 = 0

=> 8(m-4)^4 - 6(m-4)^2 - 4(m-4)^2 + 3 = 0

=>(4(m-4)^2 -3)(2(m-4)^2-1) = 0

=>((m-4)^2 -3/4)((m-4)^2-1/2) = 0

=>(m-4-sqrt(3)/2)(m-4+sqrt(3)/2)(m-4-1/sqrt(2))(m-4+1/sqrt(2))=0

=>m = 4+sqrt(3)/2, 4-sqrt(3)/2, 4+1/sqrt(2), 4-1/sqrt(2)