Question 61864
<pre>Can you help solve this equation?
3x^2+9bx=ax +3ab
So far I've tried
3x^2+9bx-ax-3ab=0
-(a-3x)(3b+x)=0
I am to solve for x
Thanks

<font size = 5 color = "crimson"><b>

Here is another (harder) way to do it using the
quadratic formula:

3x² + 9bx = ax + 3ab

Get all terms on the left

3x² + 9bx - ax - 3ab = 0

Factor x out of the middle two terms

3x² + x(9b - a) - 3ab = 0

Rewrite the middle term x(9b - a) as (9b - a)x

3x² + (9b - a)x - 3ab = 0

Now this is in the form:

Ax² + Bx + C = 0

where A = 3, B = (9b - a) and C = -3ab

Notice that I used capital letters A, B, 
and C to prevent confusion with the small 
letters a and b in your equation:

Use the quadratic formula:
                  ______ 
            -B ± <font face = "symbol">Ö</font>B²-4AC
        x = —————————————
                2A 

                        __________________  
             -(9b-a) ± <font face = "symbol">Ö</font>(9b-a)²-4(3)(-3ab)
        x = ———————————————————————————————
                        2(3) 


                        ____________  
             -(9b-a) ± <font face = "symbol">Ö</font>(9b-a)²+36ab
        x = ————————————————————————————
                        6 

                        _________________  
             -(9b-a) ± <font face = "symbol">Ö</font>(9b-a)(9b-a)+36ab
        x = ———————————————————————————————
                          6 
      
                        _________________  
             -(9b-a) ± <font face = "symbol">Ö</font>81b²-18ab+a²+36ab
        x = ———————————————————————————————
                          6 

                        ____________  
             -(9b-a) ± <font face = "symbol">Ö</font>81b²+18ab+a²
        x = ——————————————————————————
                        6

                        ____________  
             -(9b-a) ± <font face = "symbol">Ö</font>(9b+a)(9b+a)
        x = ——————————————————————————
                        6

                        _______  
             -(9b-a) ± <font face = "symbol">Ö</font>(9b+a)²
        x = —————————————————————
                     6

                          
             -(9b-a) ± (9b+a)
        x = —————————————————————
                     6

                      
Using the +,

             -(9b-a) + (9b+a)
        x = —————————————————————
                     6

             -9b + a + 9b + a
        x = ——————————————————
                     6

             2a
        x = ————
             6

             a
        x = ———
             3


Using the -,

             -(9b-a) - (9b+a)
        x = —————————————————————
                     6

             -9b + a - 9b - a
        x = ——————————————————
                     6

             -18b
        x = ——————
               6

               
        x = -3b
             
So the two solutions are 

             a
        x = ———  and  x = -3b
             3

Edwin</pre>