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!