SOLUTION: What is the value of the discriminant and also the nature of the roots of the equation {{{5n^2=4n+6}}}

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Question 8627: What is the value of the discriminant and also the nature of the roots of the equation 5n%5E2=4n%2B6
Answer by glabow(165) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant is the value sqrt%28b%5E2+-+4ac%29 where a, b, and c are the coefficients of the quadratic equation in the standard form ax%5E2%2Bbx%2Bc.
This means you want to first rearrange the equation you have to standard form.
5n%5E2=4n%2B6
5n%5E2+-4n-6=0 [adding -4n-6 to both sides]
So, a=5, b=-4, and c=-6
The discriminant is sqrt%28%28%28-4%29%28-4%29%29+-+%28%284%29%285%29%28-6%29%29%29
which is sqrt%2816%2B120%29=sqrt%28136%29=11.66 or so.
This tells you that the solutions of the equation are both real.
This is clear also from the graph of the equation
graph%28500%2C+500%2C+-5%2C+5%2C+-10%2C+10%2C+5x%5E2-4x-6%29