The problem is to solve the equation $3 + \sqrt{4x - 5} = 8$ for $x$.

1. Problem Description

The problem is to solve the equation $3 + \sqrt{4x - 5} = 8$ for $x$.

2. Solution Steps

First, isolate the square root term by subtracting 3 from both sides of the equation:

$3 + \sqrt{4x - 5} - 3 = 8 - 3$

$\sqrt{4x - 5} = 5$

Next, square both sides of the equation to eliminate the square root:

$(\sqrt{4x - 5})^2 = 5^2$

$4x - 5 = 25$

Add 5 to both sides of the equation:

$4x - 5 + 5 = 25 + 5$

$4x = 30$

Divide both sides of the equation by 4 to solve for $x$:

$\frac{4x}{4} = \frac{30}{4}$

$x = \frac{15}{2}$

3. Final Answer

$x = \frac{15}{2}$