SOLUTION: forty five people cashed check at bank A on monday. of these, 80% already had accounts at bank A. one-third of the people who did not already have an account opened an account on m

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Question 298615: forty five people cashed check at bank A on monday. of these, 80% already had accounts at bank A. one-third of the people who did not already have an account opened an account on monday. how many people opened an account on monday?
Answer by Jeff Gordon(65) 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 1x%5E2%2B-2x%2B-3+=+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%2A1%2A-3=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%28-2%29-sqrt%28+16+%29%29%2F2%5C1+=+-1

Quadratic expression 1x%5E2%2B-2x%2B-3 can be factored:
1x%5E2%2B-2x%2B-3+=+1%28x-3%29%2A%28x--1%29
Again, the answer is: 3, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-3+%29