The relationship between Young's modulus Y, Bulk modulus K and modulus of rigidity η is
Y=9ηKη+3K
η=9YKY+3K
Y=9ηK3+K
Y=3ηK9η+K
Y=3K(1−2σ) and Y=2η(1+σ)
Eliminating σ we get Y=9ηKη+3K