Find the solution(s) of 3(x^2)-6x+2=0

This is a quadratic equation and as such it has zero, one or two solutions depending on the value of the discriminant (b²-4ac). In this equation, a=3, b=-6 and c=2 so b²-4ac = 36-24=12. As this is >0 the equation has two real solutions, however this is not a square number and therefore we cannot factorise and will have to use the quadratic formula. This is (-b (+/-) (b²-4ac)^1/2)/(2a). Subsituting in a, b and c gives us (6 (+/-) 12^1/2)/6 which means our two solutions are x=1+(1/6)12^1/2and x=1-(1/6)12^1/2