Question 137329
{{{sqrt(5x+21)=x+3}}}
First step, square both sides to get rid of the radical. 
{{{5x+21=(x+3)^2}}} 
Expand the right hand side.
{{{5x+21=x^2+6x+9}}}
Bring all terms over to the left hand side.
{{{5x+21-x^2-6x-9=0}}}
{{{-x^2-x+12=0}}}
Multiply both sides by -1.
{{{x^2+x-12=0}}}
Factor your quadratic equation.
{{{(x+4)(x-3)=0}}}
x=-4 and x=3 are both solutions.
Check your answers.
x=3
{{{sqrt(5x+21)=x+3}}}
{{{sqrt(5(3)+21)=3+3}}}
{{{sqrt(15+21)=6}}}
{{{sqrt(36)=6}}}
{{{6=6}}}
True statement. Good answer.
x=-4
{{{sqrt(5(-4)+21)=-4+3}}}
{{{sqrt(-20+21)=-1}}}
{{{sqrt(1)=-1}}}
True statement, since {{{(-1)^2=1}}}.
Good answer.