The circuit has 2R and X in series (top branch) parallel to R (bottom branch).
The equivalent resistance is Req=3R+X(2R+X)⋅R=X.
Setting up the equation: X(3R+X)=R(2R+X), which simplifies to X2+2RX−2R2=0.
Using the quadratic formula: X=2−2R±2R3=R(−1±3).
Since resistance must be positive, X=(3−1)R Ω.
