SOLUTION: I am supposed to solve this: 3x^2 - 7x - 13=0 What are the solutions? I think the answer is there are no solutions,because 7x and 13 are negative. Am I right?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am supposed to solve this: 3x^2 - 7x - 13=0 What are the solutions? I think the answer is there are no solutions,because 7x and 13 are negative. Am I right?      Log On


   

Question 232806: I am supposed to solve this:
3x^2 - 7x - 13=0
What are the solutions?

I think the answer is there are no solutions,because 7x and 13 are negative. Am I right?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2 - 7x - 13=0
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There are always solutions, tho they might not be real numbers.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-7x%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=%28-7%29%5E2-4%2A3%2A-13=205.

Discriminant d=205 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+205+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+205+%29%29%2F2%5C3+=+3.55297017721273
x%5B2%5D+=+%28-%28-7%29-sqrt%28+205+%29%29%2F2%5C3+=+-1.21963684387939

Quadratic expression 3x%5E2%2B-7x%2B-13 can be factored:
3x%5E2%2B-7x%2B-13+=+%28x-3.55297017721273%29%2A%28x--1.21963684387939%29
Again, the answer is: 3.55297017721273, -1.21963684387939. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-7%2Ax%2B-13+%29