SOLUTION: help me solve 4v^2-17=3v

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Question 444569: help me solve 4v^2-17=3v
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
4v^2-17=3v
4v^2-3v-17=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation av%5E2%2Bbv%2Bc=0 (in our case 4v%5E2%2B-3v%2B-17+=+0) has the following solutons:

v%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%2A4%2A-17=281.

Discriminant d=281 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+281+%29%29%2F2%5Ca.

v%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+281+%29%29%2F2%5C4+=+2.47038182678003
v%5B2%5D+=+%28-%28-3%29-sqrt%28+281+%29%29%2F2%5C4+=+-1.72038182678003

Quadratic expression 4v%5E2%2B-3v%2B-17 can be factored:
4v%5E2%2B-3v%2B-17+=+4%28v-2.47038182678003%29%2A%28v--1.72038182678003%29
Again, the answer is: 2.47038182678003, -1.72038182678003. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-3%2Ax%2B-17+%29