Question 368354
Use a substitution, {{{u=root(5,x+2))}}}
{{{u^2-6u=-8}}}
{{{u^2-6u+8=0}}}
{{{(u-2)(u-4)=0}}}
Two solutions:
{{{u-2=0}}}
{{{u=2}}}
{{{root(5,x+2)=2}}}
{{{x+2=2^5}}}
{{{highlight(x=30)}}}
.
.
.
{{{u-4=0}}}
{{{u=4}}}
{{{root(5,x+2)=4}}}
{{{x+2=4^5}}}
{{{highlight(x=1022)}}}