Algebra 

minimum value of (4y² – 12y + 25) is 16,   so 4y² – 12y + 25>= 16

hence (4x² + 6x + 4) =< 7/4 ; 

but minimum value of 4x² + 6x + 4 is 7/4

7/4 and 16 are the minimum possible values of these two expressions
Hence only one solution is possible.