Please Help Melody! i edited it

Present it properly, by editing it, and I will think about helping you.  But you need to be quick, 

x(3x-4) <= (6x^2-3x+5)/10

30x^2 -40x  <= 6x^2 - 3x +5

24x^2-37x-5 <=0   this is a bowl shaped parabola with zeroes (via quadratic formula) at 1.64 and -.101   

                                  it is negative in between the zeroes..

                                     .this includes the integers      0 and 1

confusion

That is much better. And no the answer is not 6.

\(x(3x-4) \le \frac{(6x^2-3x+5)}{10}\\ 10x(3x-4) \le 6x^2-3x+5\\ \)

Now you have to expand the left-hand side

then

take all the terms to the left side so that it is   <=0

then

Factorise the left side.

Now if you let the left side equal y

then y must be less than or equal to 0

The left side, when you put it equal to y, will actually be a concave up parabola.

Find the roots of the parabola.

Any integers between the roots will be solutions to this problem.   :)

Give it a go