To solve this equation, we need to isolate x on one side of the equation.

Given equation:

x + 6/(x - 6)^0.5= √(3x + 2)

First, let's square both sides of the equation to get rid of the square root:

(x + 6/(x - 6)^0.5)^2 = 3x + 2

Expanding the left side:

(x^2) + 2x(6/(x - 6)^0.5) + 6^2 / (x - 6) + 36 / (x - 6) + 36/(x - 6) = 3x + 2

Now simplify:

x^2 + 12 + 36/(x - 6) + 36/(x - 6) = 3x + 2

Combine like terms:

x^2 - 3x + 46 = 72/(x - 6)

Now let's solve for x. We will first multiply through by (x - 6) to get rid of the denominator:

x^3 - 3x^2 + 46x - 6x^2 + 18x - 276 = 72

Rearrange the equation:

x^3 - 9x^2 + 64x - 348 = 0

This is a cubic equation, which can be solved using various methods such as factoring, synthetic division, or a numerical method (like Newton's method). Without further information on how to proceed, it's not possible to give an exact solution at this point.