  We prove an analog of the wall crossing formula for Welschinger invariants
relating the difference of signed curve counting of real curves passing through
configurations that differ by a pair of complex conjugated points, and a
correspondence Welschinger invariant of the blow up.
  We prove this analogue for the motivic count of rational curves of fixed
degree passing through a generic configuration of points, counted with a
motivic multiplicity in the Grothendieck-Witt ring of a base field, extending
the notions in the correspondence theorem between motivic invariants for
$k$-rational point conditions and tropical curves.
  We use this formula to compute the degree 4 motivic enumerative invariants of
the projective plane counting curves passing through configurations of points
defined over quadratic extensions of a base field.
