SOLUTION: solve by using quadratic formula. 6x^2=3x-2

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Question 344534: solve by using quadratic formula. 6x^2=3x-2
Found 2 solutions by JBarnum, ewatrrr:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
6x^2-3x+2=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-3x%2B2+=+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=%28-3%29%5E2-4%2A6%2A2=-39.

The discriminant -39 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -39 is + or - sqrt%28+39%29+=+6.2449979983984.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-3%2Ax%2B2+%29

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
6x^2=3x-2
Put is the form of a quadratic equation:
6x%5E%282%29-3x+%2B2+=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-3x%2B2+=+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=%28-3%29%5E2-4%2A6%2A2=-39.

The discriminant -39 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -39 is + or - sqrt%28+39%29+=+6.2449979983984.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-3%2Ax%2B2+%29