SOLUTION: how would i solve this equation i dont uderstand it 9x^2+6x+3=0

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Question 359091: how would i solve this equation i dont uderstand it 9x^2+6x+3=0
Found 2 solutions by Fombitz, vleith:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
9x%5E2%2B6x%2B3=0
a=9
b=6
c=3
Use the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A9%2A3+%29%29%2F%282%2A9%29+
x+=+%28-6+%2B-+sqrt%28+36-108+%29%29%2F%2818%29+
Complete the calculation to get the solutions.

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
9x%5E2%2B6x%2B3=0
3%2A%283x%5E2+%2B+2x+%2B+1%29+=+0
%283x%5E2+%2B+2x+%2B+1%29+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B2x%2B1+=+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=%282%29%5E2-4%2A3%2A1=-8.

The discriminant -8 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 -8 is + or - sqrt%28+8%29+=+2.82842712474619.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B2%2Ax%2B1+%29