2sin^2α-cos^α+sinα*cosα-6sinα+3cosα=0
(2sinα-cosα)(sinα+cosα)-3(2sinα-cosα)=0
(2sinα-cosα)(sinα+cosα-3)=0
sinα+cosα=√2sin(α+π/4)<=√2
所以sinα+cosα-3<0
2sinα-cosα=0
cosα=2sinα
代入sin^2α+cos^2α=1
sin^2α=1/5
cos^2α=4/5
2sinαcosα
=2sinα*2sinα
=4sin^2α
=4/5
cosα=2sinα
tanα=sinα/cosα=1/2
所以原式=8/5