SOLUTION: What is the answer for the equation 6x^2-x-1

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Question 734966: What is the answer for the equation 6x^2-x-1
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
there is no equation. Equations have equal signs. Do you see an equal sign?
set it equal to zero
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-1x%2B-1+=+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=%28-1%29%5E2-4%2A6%2A-1=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+25+%29%29%2F2%5C6+=+0.5
x%5B2%5D+=+%28-%28-1%29-sqrt%28+25+%29%29%2F2%5C6+=+-0.333333333333333

Quadratic expression 6x%5E2%2B-1x%2B-1 can be factored:
6x%5E2%2B-1x%2B-1+=+%28x-0.5%29%2A%28x--0.333333333333333%29
Again, the answer is: 0.5, -0.333333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-1%2Ax%2B-1+%29



x=1/2 x=-1/3