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First you look at the question and observe it once or twice before actually doing something about it. We see that 4 is common on both the sides.

So we divide by 4 on both sides and 4 is cancelled. we are left with x-9=9+1/3x. we take 9 on the other side

x=9+9+1/3x

next we have x=18+1/3x

take least common factor of 3x and we get

x=(18*3x+1)/3x

we multiply 3x on both sides and we get

x*3x=54x+1

this gives us the quadratic equation :

3x^2 - 54x -1=0

applying the quadratic formula (-b+-SQRT(b^2-4*a*c))/(2*a)

where a=3, b=-54 and c=-1

giving 2 answers those are: 18.01 and -0.018

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

hello peeps
I am attaching the solution of this question 

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

=> x-9=9+x/3

=>2x/3=18

=>x=27

Hope it helps, All the best.

Is that 1/(3x) or (1/3)*x?

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