SOLUTION: How do I solve this equation: f(x)= 24x^2+2x=29

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Question 661094: How do I solve this equation:
f(x)= 24x^2+2x=29
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,




 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 24x%5E2%2B2x%2B-29+=+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=%282%29%5E2-4%2A24%2A-29=2788.

  

  Discriminant d=2788 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+2788+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%282%29%2Bsqrt%28+2788+%29%29%2F2%5C24+=+1.05836489853701

    x%5B2%5D+=+%28-%282%29-sqrt%28+2788+%29%29%2F2%5C24+=+-1.14169823187034

    

    Quadratic expression 24x%5E2%2B2x%2B-29 can be factored:

  24x%5E2%2B2x%2B-29+=+24%28x-1.05836489853701%29%2A%28x--1.14169823187034%29

  Again, the answer is: 1.05836489853701, -1.14169823187034.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+24%2Ax%5E2%2B2%2Ax%2B-29+%29