SOLUTION: It has been 20+ years and algebra still makes me phisically sick. I am stumped on the silliest of things. 1/3(2a-8)-7 = 2/5a The common denominator (as far as I can tell) is

Make the denominator of  the same as the denominator of .

Just times  but some number to get its denominator to 3. In this case, we just times 1 (the denominator by 3 in order to get its overall denominator to 3.

Whatever we do the the denominator, must also be done to the numerator. We have times the denominator by 3 and therefore, we must also times the numerator by 3.

We end up with 

Now we have:



We can join up the fractions on the left hand side as they have common denominators.



This gives us:



Whenever we get this in maths, (a technique I have always used), we cross multiply.

So from, 

We get,



We can now multiply out the brackets.



Rearrange the equation:



This is a quadratic equation.

 
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation  (in our case ) has the following solutons:
  
  
  
  For these solutions to exist, the discriminant  should not be a negative number.
  
  First, we need to compute the discriminant : .
  
  Discriminant d=21265 is greater than zero. That means that there are two solutions: .
  
    
    
    
    Quadratic expression  can be factored:
  
  Again, the answer is: 14.5412618935271, -0.0412618935270729.
Here's your graph:




x = 14.5412618935271, -0.0412618935270729