Question 135472
{{{x+2=root(3,12x+2)}}} Start with the given equation



{{{(x+2)^3=12x+2}}} Cube both sides



{{{x^3+6x^2+12x+8=12x+2}}} Expand the left side




{{{x^3+6x^2+12x+8-12x-2=0}}}  Subtract 12x from both sides.  Subtract 2 from both sides. 



{{{x^3+6x^2+6=0}}} Combine like terms



So from a graphing calculator, we find that the solution to {{{x^3+6x^2+6=0}}} is {{{x=-6.15821}}}