Answer
$x=\dfrac{4}{3}$
Work Step by Step
Subtract 4 from both sides:
$4-4+\sqrt{3x+5}=7-4$
$\sqrt{3x+5}=3$
Square both sides:
$(\sqrt{3x+5})^2=(3)^2$
$3x+5=9$
Subtract $5$ from both sides:
$3x+5-5=9-5$
$3x=4$
Divide both sides by $3$:
$\dfrac{3x}{3}=\dfrac{4}{3}$
$x=\dfrac43$
Substitute into original problem to check for extraneous solutions:
$4+\sqrt{3\left(\frac{4}{3}\right)+5}=7$
$4+\sqrt{4+5}=7$
$4+\sqrt{9}=7$
$4+3=7$
$7=7$
