find all possible functions : $f(a)f(b)-6ab=\frac{3}{2}f(a+b)$ I'm trying to find all possible functions that satisfy this functional equation: 
$f(a)f(b)-6ab=\frac{3}{2}f(a+b),$
$f\in \mathbb{R}.$ 
My attempt : 
$a=b=0$ then $f(0)=0$ or $1.$
But I don't have any ideas to complete .
Please give me hints.

Making $f(x) = a x + b$ and substituting we have
$$
f(x)f(y)-6xy-\frac 32 f(x+y)=(a^2-6)xy+\left(ab-\frac{3a}{2}\right)(x+y)+b^2-\frac{3b}{2}=0
$$
giving
$$
f(x) = \sqrt 6 x+\frac 32
$$
which is also a solution.
