My Calc teacher, well, he's cruel. Hard problem..

Given that $\displaystyle f(x) = 3x² + x / 2x -1$ , find all of the points on the curve where the tangent line has to behorizontal and vertical.

I first solved the derivative of the equation to get6x ²-6x-1 / (2x-1)².

From there, do I solve where the numerator is 0 (horizontal) and where the denominator is 0 (vertical)?

Thank you. I seem stuck, as always...