SOLUTION: what are the solutions to the quadratic equation y^2 -3y=9 ??

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Question 393597: what are the solutions to the quadratic equation y^2 -3y=9 ??
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
y^2 -3y=9
y^2 -3y-9=0
solve by applying the "quadratic equation". Doing so, yields:
y = {4.854, -1.854}
.
Details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 1y%5E2%2B-3y%2B-9+=+0) has the following solutons:

y%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=%28-3%29%5E2-4%2A1%2A-9=45.

Discriminant d=45 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+45+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+45+%29%29%2F2%5C1+=+4.85410196624968
y%5B2%5D+=+%28-%28-3%29-sqrt%28+45+%29%29%2F2%5C1+=+-1.85410196624968

Quadratic expression 1y%5E2%2B-3y%2B-9 can be factored:
1y%5E2%2B-3y%2B-9+=+1%28y-4.85410196624968%29%2A%28y--1.85410196624968%29
Again, the answer is: 4.85410196624968, -1.85410196624968. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-9+%29