Question 907261
{{{9x^2+1>=6x}}}
{{{9x^2-6x+1>=0}}}


Roots are these.
{{{(6-sqrt(36-4*9*1))/18}}} and {{{(6+sqrt(36-4*9*1))/18}}} which are equal because the discriminant is 0.
Only one root:  {{{6/18=1/3}}}.


The inequality is true for all real values of x.


{{{graph(300,300,-4,4,-2,4,9x^2-6x+1)}}}


You could factorize the quadratic trinomial, since you found the single root of {{{x=1/3}}}.  Not so easy to recognize without actually evaluating the discriminant.


{{{9(x^2-(6/9)x+1/9)>=0}}}
{{{highlight(9(x-1/3)^2>=0)}}}