SOLUTION: I need help solving this quadratic equation. Every answer that I get looks nothing like the answer in the book. f(x)= -6x^2+8x+9

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Question 433773: I need help solving this quadratic equation. Every answer that I get looks nothing like the answer in the book.
f(x)= -6x^2+8x+9
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -6x%5E2%2B8x%2B9+=+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=%288%29%5E2-4%2A-6%2A9=280.

Discriminant d=280 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+280+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+280+%29%29%2F2%5C-6+=+-0.727766710890126
x%5B2%5D+=+%28-%288%29-sqrt%28+280+%29%29%2F2%5C-6+=+2.06110004422346

Quadratic expression -6x%5E2%2B8x%2B9 can be factored:
-6x%5E2%2B8x%2B9+=+%28x--0.727766710890126%29%2A%28x-2.06110004422346%29
Again, the answer is: -0.727766710890126, 2.06110004422346. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-6%2Ax%5E2%2B8%2Ax%2B9+%29