SOLUTION: Sove an equation: 3z^2-8z+2=0

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Question 326813: Sove an equation:
3z^2-8z+2=0
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation az%5E2%2Bbz%2Bc=0 (in our case 3z%5E2%2B-8z%2B2+=+0) has the following solutons:

z%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=%28-8%29%5E2-4%2A3%2A2=40.

Discriminant d=40 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+40+%29%29%2F2%5Ca.

z%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+40+%29%29%2F2%5C3+=+2.38742588672279
z%5B2%5D+=+%28-%28-8%29-sqrt%28+40+%29%29%2F2%5C3+=+0.279240779943873

Quadratic expression 3z%5E2%2B-8z%2B2 can be factored:
3z%5E2%2B-8z%2B2+=+3%28z-2.38742588672279%29%2A%28z-0.279240779943873%29
Again, the answer is: 2.38742588672279, 0.279240779943873. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-8%2Ax%2B2+%29