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Verified answer

4(x²-x)²+9(x²-x)+2=0,
x²-x=a,
4a²+9a+2=0,
D=49, a₁=-2, a₂=-¹/₄,
x²-x=-2,
x²-x+2=0,
D=-7<0, нет решений,
x²-x=-¹/₄,
4x²-4x+1=0,
(2x-1)²=0,
2x-1=0,
x=¹/₂.