#### Answer

a=7

#### Work Step by Step

Recall, in order to cancel out a square root, we square both sides of the equation. Thus, we square both sides of the equation to obtain that 4a+3=5a-4. We now simplify:
$ 3=a-4 \\\\ a=7$
We now must check our solution:
$\sqrt{4(7)+3}=\sqrt{5(7)-4} \\\\ \sqrt{31}=\sqrt{31} $
This is true, so our solution is valid.