An inefficient root finder

Algebra Level 5

$f( x ) =( { x }^{ 2 }+A ) ( { x }^{ 2 }+B )$

If $$B-A=456$$, find a real root for $$f( x )$$ that satisfies the relation below, where $$C$$ is a real, arbitrary constant.

$x=\left( 1+i \right) \sqrt [ 4 ]{ \frac { 3 }{ 2 } { x }^{ 2 }+C }$

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