Solve by factoring

3x squared + 6x + 2 = 0

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Solve `3x^2+6x+2=0` :

`3x^2+6x+2=0`

``This does not factor in the rationals. We can use completing the square or the quadratic formula to solve.

`3(x^2+2x+2/3)=0`

`3(x^2+2x+1-1+2/3)=0`

`3((x+1)^2-1/3)=0`

`3(x+1)^2-1=0`

`(x+1)^2=1/3`

`x+1=+-sqrt(1/3)`

`x=-1+-sqrt(3)/3`

`3x^2+6x+2=0`

`Delta= 36-4xx3xx2=12>=0`

Has two different real solutions:

`x=(-6+-sqrt(12))/6=(-6+-2sqrt(3))/6=(-3+-sqrt(3))/3`

`x_1=(sqrt(3)-3)/3` `x_2=-(3+sqrt(3))/3`

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