SOLUTION: 18 secx^2-17 secxtanx-12=0 can you help me solve this?

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Question 1034228: 18 secx^2-17 secxtanx-12=0 can you help me solve this?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
18secx^2- 17secxtanx - 12 = 0
Multiply thru by cos^2
18 - 17sin(x) - 12cos^2(x) = 0
12cos^2 + 17sin - 18 = 0
cos^2 = 1 - sin^2
12sin^2 - 17sin + 6 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B-17x%2B6+=+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=%28-17%29%5E2-4%2A12%2A6=1.

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

x%5B1%5D+=+%28-%28-17%29%2Bsqrt%28+1+%29%29%2F2%5C12+=+0.75
x%5B2%5D+=+%28-%28-17%29-sqrt%28+1+%29%29%2F2%5C12+=+0.666666666666667

Quadratic expression 12x%5E2%2B-17x%2B6 can be factored:
12x%5E2%2B-17x%2B6+=+%28x-0.75%29%2A%28x-0.666666666666667%29
Again, the answer is: 0.75, 0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B-17%2Ax%2B6+%29

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sin(x) = 3/4, 2/3