First off, you divide both sides by 4

4/4(x-9)=4/4(9+1/3x)

=> x-9=9+1/3x

Then, you add 9 on both sides

=> x-9+9=9+9+1/3x

=> x=18+1/3x

Then, you substract 1/3x from both sides

=> x-1/3x=18+1/3x-1/3x

=> x-1/3x=18

Now, you solve the sum on the left side. If it is (1/3)*x, then

=> 3/3x-1/3x=18

=> 2/3x=18

Finally, divide both sides by 2/3

=> 2/3/(2/3)x=18/(2/3)

=> x=18*3/2

=> x=27

If it is 1/(3*x), it is a little more complicated;

At this point, you substract 18 from both sides:

=> x=18+1/3x

=> x-18=18-18+1/3x

=> x-18=1/3x

Then, you multiply both sides times "x"

=> (x-18)*x=(1/3x)*x

=> x^2-18*x=1/3

Then, you substract 1/3 from both sides

=> x^2-18*x-1/3=1/3-1/3

=> x^2-18*x-1/3=0

At this point, you should be able to apply the formula to solve quadratic equations: (-b+-SQRT(b^2-4*a*c))/(2*a), where a=1,b=-18 and c=-1/3

=>(-(-18)+-SQRT((-18)^2-4*1*(1/3)))/(2*1)

Then you solve both cases (+ and - SQRT), and you should have 2 answers

=>(-(-18)+SQRT((-18)^2-4*1*(1/3)))/(2*1)

=>(18+SQRT(324-4/3))/2

=>(18+SQRT((972-4)/3))/2

=>(18+SQRT(968/3))/2

Then, your both answers are:

(18+SQRT(968/3))/2

(18-SQRT(968/3))/2