SOLUTION: Solve. 2y^2 – y – 3 = 0 Thanks!

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Question 40706: Solve.
2y^2 – y – 3 = 0
Thanks!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2y^2 – y – 3 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 2y%5E2%2B-1y%2B-3+=+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=%28-1%29%5E2-4%2A2%2A-3=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+25+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+25+%29%29%2F2%5C2+=+1.5
y%5B2%5D+=+%28-%28-1%29-sqrt%28+25+%29%29%2F2%5C2+=+-1

Quadratic expression 2y%5E2%2B-1y%2B-3 can be factored:
2y%5E2%2B-1y%2B-3+=+2%28y-1.5%29%2A%28y--1%29
Again, the answer is: 1.5, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-1%2Ax%2B-3+%29

Cheers,
Stan H.