There are 3 forces acting on the beam.

Weight, tension at A, tension at C. You should have gotten

C = 140

A = 70

The beam is in equilibrium, which means no movement. No moments about any point.

No moments about point B!

Let distance CB = x

Moment about B, from force at C:

Moment about B from force at A:

Moment from weight(which acts at the centre):

The sum of these should be zero, and then you have an equation in x to solve!

Remember that anticlockwise moments are positive, and clockwise moments are negative!