#### Answer

$x=-2$ or $x=-1$

#### Work Step by Step

Add 3 on both sides of the equation to obtain:
$x+3=\sqrt{3x+7}$
Square both sides of the equation to obtain:
$(x+3)^2=3x+7$
Use the rule $(a+b)^2 = a^2 + 2ab+b^2$ where $a=x$ and $b=3$ to obtain:
$\\x^2+6x+9=3x+7$
Move all terms to the left side of the equation. Note that when a term is moved to the other side of the equation, its sign changes to its opposite.
$x^2+6x+9-3x-7=0
\\x^2+3x+2=0$
Factor the trinomial to obtain:
$(x+2)(x+1)=0$
Equate each factor to zero then solve each equation to obtain:
$x+2 = 0 \text{ or } x + 1 = 0
\\x = -2 \text{ or } x = -1$