SOLUTION: Can you please solve this 3x^2-5x-13=0

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Question 260425: Can you please solve this 3x^2-5x-13=0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
This can't be factored with whole numbers
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-5x%2B-13+=+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-13=181.

Discriminant d=181 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+181+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+181+%29%29%2F2%5C3+=+3.07560400784562
x%5B2%5D+=+%28-%28-5%29-sqrt%28+181+%29%29%2F2%5C3+=+-1.40893734117895

Quadratic expression 3x%5E2%2B-5x%2B-13 can be factored:
3x%5E2%2B-5x%2B-13+=+3%28x-3.07560400784562%29%2A%28x--1.40893734117895%29
Again, the answer is: 3.07560400784562, -1.40893734117895. 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-13+%29