#### Answer

$\color{blue}{x=3, x=-1}$

#### Work Step by Step

Add $9$ to both sides to obtain:
$\sqrt{6x+7}=x+2$
Square both sides to obtain:
$6x+7=(x+2)^2
\\6x+7=x^2+2(x)(2)+2^2
\\6x+7=x^2+4x+4$
Move all terms to the left side of the equation.
Note that when a term is transferred to the other side of the equation, its sign changes to its opposite.
$0=x^2+4x+4-6x-7
\\0=x^2-2x-3
\\x^2-2x-3=0$
Factor the trinomial to obtain:
$(x-3)(x+1)=0$
Use the zero-factor property by equating each factor to zero.
$x-3=0$ or $x+1=0$
Solve each equation to obtain:
$x=3$ or $x=-1$.
Upon checking, both proposed solutions satisfy the original equation.
Thus, the solutions to the given equation are $\color{blue}{x=3, x=-1}$.