Question 284863
Completing the square.
{{{3x^2-6x-2=0}}}
{{{x^2-2x-(2/3)=0}}}
Take (1/2) of the x coefficient, square it, add it to both sides.
{{{(x^2-2x+1)-(2/3)=1}}}
{{{(x-1)^2-(2/3)=1}}}
{{{(x-1)^2=1+2/3=3/3+2/3=5/3}}}
Take the square root of both sides. 
{{{(x-1)=0 +- sqrt(5/3)}}}
{{{x=1 +- sqrt(5/3)}}}
{{{x=1 +- sqrt(15)/3)}}}
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Quadratic formula.
a=3
b=-6
c=-2
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (6 +- sqrt( (-6)^2-4*3*(-2) ))/(2*3) }}}
{{{x = (6 +- sqrt( 36+24 ))/(6) }}}
{{{x = (6 +- sqrt(60))/(6) }}}
{{{x = (6 +- sqrt(4*15))/(6) }}}
{{{x = (6 +- 2*sqrt(15))/(6) }}}
{{{x = 1 +- sqrt(15)/3 }}}