Find vertical tangent lines of $\displaystyle y=(2x-6)/(sqrt x^2+3)$.(how do you do square root symbols?)

$\displaystyle y'=[(12-12x)/(2sqrtx^2+)]/(x^2+3)$

$\displaystyle (x^2+3)=0$

$\displaystyle x=+or- (-sqrt3)$, x=complex number, so there are no vertical tangent lines?

Edit: Or actually, $\displaystyle (x^2+3)$ will never be zero, so the denominator would have to be a root function or a fraction to be a vertical tangent line?