Find intersection point in a road network of line shapefile

Ok, that's the steps you need to folow.

1. First use Dissolve without any attribute on your road layer.
2. Next on dissolve layer use "Multipart to single parts" tool.
3. After that use "Line intersection" on output from previous step.

I am not sure if i translate it correctly because not i am using polish version of QGIS. You can find in Vector toolbox.

After that just select same feature line twice without any unic fields.

EDIT

Ok i see that Dissolve in Qgis is a bit different that Dissolve in ArcGIS. But to work around it i came up with this idea.

1. First Save As.. your existing shape file to work on copy.
2. Next edit copy feature, select all lines and merge them together using "Merge Selected Features" from Advance Digitizing Toolbar and save it.
3. Then use "Multipart to single parts" tool.
4. After that use "Line intersection" on output from previous step.