Answer
The equation has no solution.
Work Step by Step
$\sqrt{x+7}+3=\sqrt{x-4}$
Square both sides of the equation:
$(\sqrt{x+7}+3)^{2}=(\sqrt{x-4})^{2}$
$x+7+6\sqrt{x+7}+9=x-4$
Leave the square root term alone on the left side of the equation:
$6\sqrt{x+7}=x-4-x-7-9$
$6\sqrt{x+7}=-20$
Take $6$ to divide the right side:
$\sqrt{x+7}=-\dfrac{20}{6}$
$\sqrt{x+7}=-\dfrac{10}{3}$
Square both sides:
$(\sqrt{x+7})^{2}=\Big(-\dfrac{10}{3}\Big)^{2}$
$x+7=\dfrac{100}{9}$
Solve for $x$:
$x=\dfrac{100}{9}-7$
$x=\dfrac{37}{9}$
The value of $x$ found is not a solution for the equation, it has no solution.
