Let two equal charges Q each be held at A and B, where AB = 2x. C is the centre of AB, where charge q is held. Net force on q is zero. So, q is already in equilibrium.
For the three charges to be in equilibrium, net force on each charge must be zero.
Now, total force on Q at B is
1/44πε0. Qq/x2 + 1/44πε0. QQ/(2X)2 = 0
or 1/44πε0. Qq/x2 . 1/44πε0. Q2 /4x2
or Q =
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