How to solve a limit through rationalizing but the radicand is a linear relation and the denominator is a quadratic? The question is :

$$\lim_{x\to 0}{\frac{\sqrt {3x+4}-6}{x^2}}$$          

My friend and I are absolutely stumped and can only attempt to solve through substitution. Any ideas?
At the limit,
the numerator is non-zero and negative
and the denominator is zero.

What does that tell you?
At the limit,
the numerator is non-zero and negative
and the denominator is zero.

What does that tell you?