SOLUTION: please help me with this equation....3x^2-5x-3=0

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Question 813679: please help me with this equation....3x^2-5x-3=0
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

3x^2-5x-3=0




 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-5x%2B-3+=+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=%28-5%29%5E2-4%2A3%2A-3=61.

  

  Discriminant d=61 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+61+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+61+%29%29%2F2%5C3+=+2.13504161265111

    x%5B2%5D+=+%28-%28-5%29-sqrt%28+61+%29%29%2F2%5C3+=+-0.468374945984442

    

    Quadratic expression 3x%5E2%2B-5x%2B-3 can be factored:

  3x%5E2%2B-5x%2B-3+=+3%28x-2.13504161265111%29%2A%28x--0.468374945984442%29

  Again, the answer is: 2.13504161265111, -0.468374945984442.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-5%2Ax%2B-3+%29