Vieta's formula/Quadratic question

3x^2  + 7x + k  = 0

Let  the roots  be  a  and b

So

1/a + 1/b =  7/3

(a + b) / ab  = 7/3

The product of the roots  =   k/3

So

ab =  k/3

So

(a + b)  / (k/3)   =  7/3

3 (a + b)  =  (7/3)k

a + b  =  (7/9)k

And the sum of the roots =   -7/3

So

(-7/3) = (7/9)k

k =  (-7/3) / (7/9)  =  -3

Thank You!