SOLUTION: how do i solve this equation: 8n^3+10n^2+3n=0

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Question 693363: how do i solve this equation: 8n^3+10n^2+3n=0
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given:8n%5E3+%2B+10n%5E2+%2B+3n+=+0
Since the highet power of n is 3; there are 3 answers.
You can start by factoring out an n on the left side
n+%2A+%288n%5E2+%2B+10n+%2B+3%29+=+0
In order for the equation to equal zero, the n on the out side must equal zero.
Then you can use the quadratic equation on the part of the equation inside the parentheses.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation an%5E2%2Bbn%2Bc=0 (in our case 8n%5E2%2B10n%2B3+=+0) has the following solutons:

n%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=%2810%29%5E2-4%2A8%2A3=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+4+%29%29%2F2%5Ca.

n%5B1%5D+=+%28-%2810%29%2Bsqrt%28+4+%29%29%2F2%5C8+=+-0.5
n%5B2%5D+=+%28-%2810%29-sqrt%28+4+%29%29%2F2%5C8+=+-0.75

Quadratic expression 8n%5E2%2B10n%2B3 can be factored:
8n%5E2%2B10n%2B3+=+8%28n--0.5%29%2A%28n--0.75%29
Again, the answer is: -0.5, -0.75. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B10%2Ax%2B3+%29


So the values for n are: -0.5, -0.75 and 0