Hi

Arithmetic : d = 3







 3n^2 + n = 690

 3n^2 + n - 690 = 0

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation  (in our case ) has the following solutons:

  

  

  

  For these solutions to exist, the discriminant  should not be a negative number.

  

  First, we need to compute the discriminant : .

  

  Discriminant d=8281 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 15, -15.3333333333333.
Here's your graph:





n = 15 



 

   x = 44

check: 15(2 + 44)/2 = 345

  

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