SOLUTION: Solve using the quadratic formula. 3x^2-7x+3=0

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Question 260228: Solve using the quadratic formula.
3x^2-7x+3=0
Found 3 solutions by richwmiller, Alan3354, stanbon:
Answer by richwmiller(17219) 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 3x%5E2%2B-7x%2B3+=+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=%28-7%29%5E2-4%2A3%2A3=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+13+%29%29%2F2%5C3+=+1.767591879244
x%5B2%5D+=+%28-%28-7%29-sqrt%28+13+%29%29%2F2%5C3+=+0.565741454089335

Quadratic expression 3x%5E2%2B-7x%2B3 can be factored:
3x%5E2%2B-7x%2B3+=+3%28x-1.767591879244%29%2A%28x-0.565741454089335%29
Again, the answer is: 1.767591879244, 0.565741454089335. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-7%2Ax%2B3+%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2-7x+3=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-7x%2B3+=+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=%28-7%29%5E2-4%2A3%2A3=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+13+%29%29%2F2%5C3+=+1.767591879244
x%5B2%5D+=+%28-%28-7%29-sqrt%28+13+%29%29%2F2%5C3+=+0.565741454089335

Quadratic expression 3x%5E2%2B-7x%2B3 can be factored:
3x%5E2%2B-7x%2B3+=+%28x-1.767591879244%29%2A%28x-0.565741454089335%29
Again, the answer is: 1.767591879244, 0.565741454089335. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-7%2Ax%2B3+%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve using the quadratic formula.
3x^2-7x+3=0
-----
a = 3 ; b = -7 ; c = 3
----
x = [7 +- sqrt(49 -4*3*3)]/(2*3)
---
x = [7 +- sqrt(13)]/6
---
x = (7+sqrt(13))/6 or x = (7-sqrt(13))/6
==========================================
Cheers,
Stan H.