SOLUTION: 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

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Question 61864: 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
Found 2 solutions by funmath, Edwin McCravy:
Answer by funmath(2933)   (Show Source): You can put this solution on YOUR website!
When I factored I got (I don't know where you got the -, but you would get the same thing I got if you solved for x.) If the directions say solve, you solve for x.
(3x-a)*(x+3b)=0
3x-a=0 and x+3b=0
3x-a+a=0+a and x+3b-3b=0-3b
3x=a and x=-3b
3x/3=a/3 and x=-3b
x=a/3 and x=-3b
:
Check when x=a/3
(3(a/3)-a)(a/3+3b)=0
(a-a)(a/3+3b)=0
0(a/3+3b)=0
0=0
When x=-3b
(3(-3b)-a)(-3b+3b)=0
(-9b-a)(0)=0
0=0
We're right!!!
Happy Calculating!!!
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
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



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 ± ÖB²-4AC
        x = —————————————
                2A 

                        __________________  
             -(9b-a) ± Ö(9b-a)²-4(3)(-3ab)
        x = ———————————————————————————————
                        2(3) 


                        ____________  
             -(9b-a) ± Ö(9b-a)²+36ab
        x = ————————————————————————————
                        6 

                        _________________  
             -(9b-a) ± Ö(9b-a)(9b-a)+36ab
        x = ———————————————————————————————
                          6 
      
                        _________________  
             -(9b-a) ± Ö81b²-18ab+a²+36ab
        x = ———————————————————————————————
                          6 

                        ____________  
             -(9b-a) ± Ö81b²+18ab+a²
        x = ——————————————————————————
                        6

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

                        _______  
             -(9b-a) ± Ö(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
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