解方程 关于{x}急急急~~

{(6x+5)/8}=(81-90x)/40
(6x+5)/8 - [(6x+5)/8] = (81-90x)/40
(120x-56)/40 = [(6x+5)/8]
3x - 7/5 = [(6x+5)/8]
从而3x - 7/5 <= (6x+5)/8 < 3x - 7/5 + 1
解得41/90 < x <= 9/10
3x - 7/5为整数，由上式有-1/30 < 3x-7/5 <= 13/10
因此3x-7/5 = 0或3x-7/5 = 1解得x = 7/15或x = 4/5，检验得
x = 4/5

把分母消去
40(6x+5)=8(81-90x)
240x+200=648-720x
960x=448
x=7/15

{x}=x-[x]是什么意思?

0<={(6x+5)/8}<1,0<=(81-90x)/40<1,41<90x<=81,
0.96...<(6x+5)/8<=1.3.分两种情况讨论:
(1).0.96...<(6x+5)/8<1,{(6x+5)/8}=(6x+5)/8,
(6x+5)/8=(81-90x)/40,x=7/15.(6x+5)/8=0.975.在范围0.96...<(6x+5)/8<1内.
(2).1<=(6x+5)/8<=1.3,{(6x+5)/8}=(6x+5)/8-1=(6x-3)/8
(6x-3)/8=(81-90x)/40,x=4/5,(6x+5)/8=1.225在范围1<=(6x+5)/8<=1.3内.
方程有两个解:x=7/15和x=4/5.