For what values of k are the roots of the quadratic equation

Given:

$3 x^{2}+2 k x+27=0$

Here,

$a=3, b=2 k$ and $c=27$

It is given that the roots of the equation are real and equal; therefore, we have:

$D=0$

$\Rightarrow(2 k)^{2}-4 \times 3 \times 27=0$

$\Rightarrow 4 k^{2}-324=0$

$\Rightarrow 4 k^{2}=324$

$\Rightarrow k^{2}=81$

$\Rightarrow k=\pm 9$

$\therefore k=9$ or $k=-9$