Solution:
Steps:
(7x-2)^1/3+(7x+5)^1/3=3
1) Rewrite the equation with (7x-2)^1/3=u and x= u^3+2/7
u+(7(u^3+2/7)+5)^1/3=3
2) Solve u+(7(u^3+2/7)+5)^1/3=3 : u=1
3) Substitute back u=(7x-2)^1/3, solve for x
(7x-2)^1/3=1 : x=3/7
4) Check answer:
((7*3/7)-2)^1/3+((7*3/7)+5)^1/3=3 <<
I hoped that helped, my explanation might be a bit confusing...sorry if it is. I'm a newby, not the best at this stuff...