5. Given that the equation
$$4 x ^ { 2 } - k x + k - 3 = 0$$
where \(k\) is a constant, has real roots,
- show that
$$k ^ { 2 } - 16 k + 48 \geq 0$$
- find the set of possible values of \(k\),
- state the smallest value of \(k\) for which the roots are equal and solve the equation when \(k\) takes this value.