The solutions or roots to this equation is found by solving for x. We can do this a couple ways either by FOIL or quad formula
3x^2+6x+6=0
3(x^2+2x+2)=0
x^2+2x+2=0 we cant FOIL this out so we use the quad formula
x= [(-b+\-sqrt(b^2-4ac))/2a]
x= -2+\- sqrt(4-4(1)(2))/2(1)
x= -1 +i , -1 - i
So we have complex roots since our quad formula returned a negative number. Whenever the quad formula answer is positive we have two roots/solutions, when it is zero we have one root/solution, and whenever it is negative we have Complex roots/solutions
Hope this helps. Any questions please just ask. Thank you.