SOLUTION: Please help me solve this equation: y=4/9x2+24/9x+12

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Question 840575: Please help me solve this equation: y=4/9x2+24/9x+12

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

y=4/9x2+24/9x+12

4/9x2+24/9x+12 = 0

4x^ + 24x  + 108 = 0

 x^2 + 6x + 27 = 0

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B27+=+0) has the following solutons:

  

  x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

  

  For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

  

  First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%286%29%5E2-4%2A1%2A27=-72.

  

  The discriminant -72 is less than zero. That means that there are no solutions among real numbers.


  If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


  

      In the field of imaginary numbers, the square root of -72 is + or - sqrt%28+72%29+=+8.48528137423857. 

  

      The solution is 

  

  Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B27+%29