Finding the vertex of a line using eqn, length, midpoint

Hi,
Is it possible to find the vertices of a straight line with the following information?

1) we know the equation of the line
2) we know the length of the line
3) we know the mid-point of the line

For eg: Is it possible to find the end-points of the line?

1) y = \frac{3}{2}x - \frac{1}{2}
2) length = \sqrt{52}
3) mid point of the line is (3,4)