SOLUTION: Solve by the quadratic formula simplify answer: 4x^2+x–1=0 6x^2-2x-1=0

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Question 430968: Solve by the quadratic formula simplify answer:
4x^2+x–1=0
6x^2-2x-1=0
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B1x%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=%281%29%5E2-4%2A4%2A-1=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+17+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+17+%29%29%2F2%5C4+=+0.390388203202208
x%5B2%5D+=+%28-%281%29-sqrt%28+17+%29%29%2F2%5C4+=+-0.640388203202208

Quadratic expression 4x%5E2%2B1x%2B-1 can be factored:
4x%5E2%2B1x%2B-1+=+4%28x-0.390388203202208%29%2A%28x--0.640388203202208%29
Again, the answer is: 0.390388203202208, -0.640388203202208. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B1%2Ax%2B-1+%29

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-2x%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=%28-2%29%5E2-4%2A6%2A-1=28.

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

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+28+%29%29%2F2%5C6+=+0.607625218510765
x%5B2%5D+=+%28-%28-2%29-sqrt%28+28+%29%29%2F2%5C6+=+-0.274291885177432

Quadratic expression 6x%5E2%2B-2x%2B-1 can be factored:
6x%5E2%2B-2x%2B-1+=+6%28x-0.607625218510765%29%2A%28x--0.274291885177432%29
Again, the answer is: 0.607625218510765, -0.274291885177432. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-2%2Ax%2B-1+%29