SOLUTION: Solve by using the quadratic formula. (Enter your answers as a comma-separated list.) 24x2 − 47x − 21 = 0

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Question 773814: Solve by using the quadratic formula. (Enter your answers as a comma-separated list.)
24x2 − 47x − 21 = 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
24x2 − 47x − 21 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 24x%5E2%2B-47x%2B-21+=+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=%28-47%29%5E2-4%2A24%2A-21=4225.

Discriminant d=4225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--47%2B-sqrt%28+4225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-47%29%2Bsqrt%28+4225+%29%29%2F2%5C24+=+2.33333333333333
x%5B2%5D+=+%28-%28-47%29-sqrt%28+4225+%29%29%2F2%5C24+=+-0.375

Quadratic expression 24x%5E2%2B-47x%2B-21 can be factored:
24x%5E2%2B-47x%2B-21+=+%28x-2.33333333333333%29%2A%28x--0.375%29
Again, the answer is: 2.33333333333333, -0.375. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+24%2Ax%5E2%2B-47%2Ax%2B-21+%29