To develop the equation, follow these steps:

1. Simplify both sides of the equation:
   - Expand the terms within brackets:
     $$
     (3x−2)x  \rightarrow   3x^2-2x
     $$
     $$
     (3x−6)(2x+7)  \rightarrow   6x^2+21x-12x-42  \rightarrow   6x^2+9x-42
     $$
     The simplified equation becomes:
     $$
     3x^2-2x+6x^{1/2} = 6x^2+9x-42
     $$
     
2. Eliminate the square roots:
   - Rearrange the equation to isolate the square root term on one side and the rest on the other side:
     $$
     6x^{1/2} = 6x^2+9x-3x^2+2x-42
     $$
     $$
     6x^{1/2} = 3x^2+11x-42
     $$
   - Square both sides of the equation to remove the square root: 
     $$
     (6x^{1/2})^2 = (3x^2+11x-42)^2
     $$
     $$
     36x = (3x^2+11x-42)(3x^2+11x-42)
     $$
     $$
     36x = 3x^2(3x^2+11x-42)+11x(3x^2+11x-42)-42(3x^2+11x-42)
     $$
     $$
     36x = 3x^2\cdot \:3x^2+3x^2\cdot \:11x+3x^2\left(-42\right)+11x\cdot \:3x^2+11x\cdot \:11x+11x\left(-42\right)-42\cdot \:3x^2-42\cdot \:11x-42\left(-42\right)
     $$
     $$
     36x=9x^4+66x^3-131x^2-924x+1764
     $$
3. Solve the fourth-degree equation: 
   - Factorize the equation:
     $$
     0 \approx (x-1.9806)(x-2.7114)(x+6.0127-0.58741i)(x+6.0127+0.58741i) 
     $$
     The equation is now factored, and we can find the values of x:
     
     Real solutions:
     - $x \approx 1.9806$
     - $x \approx 2.7114$
     
     Imaginary solutions:
     - $x \approx -6.0127-0.58741i$
     - $x \approx -6.0127+0.58741i$
     
    Note: The solution values are approximations due to their infinite decimals.
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