In version 10,
RegionBounds@ImplicitRegion[x^2 + y^2 == (2 x^2 + 2 y^2 - x)^2, {x, y}](* {{-(1/8), 1}, {-((3 Sqrt[3])/8), (3 Sqrt[3])/8}} *)↧
Answer by Szabolcs for Finding maximum or minimum of implicit functions
↧