回复：美国奥赛题：一元二次方程（2.5星）

complete solution.

Step 1: determine the range of x

rewrite the euqation:
4x^2 - 40x + 51 = -40(x - [ x ])

And notice 0
hence
-40
Solve it, we get

3/2
hence:

[ x ] can only be 1 ,2, 3, 6, 7, 8

Take this equation, can easily get

x = sqrt(29)/2 OR sqrt(189)/2 OR sqrt(229)/2 OR sqrt(269)/2

In another word, only [ x ] =2,6,7,8 works