Solution:

Given quadratic equation is (a b-2c)x^2 (2a-b-c)x (c a-2b)=0

To solve this quadratic equation, we can use the quadratic formula which is given by:

For a quadratic equation of the form ax^2 + bx + c = 0, the solution is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

Here, a = a b-2c, b = 2a-b-c, and c = c a-2b

Substituting these values in the quadratic formula, we get:

x = [-(2a-b-c) ± √((2a-b-c)^2 - 4(a b-2c)(c a-2b))] / 2(a b-2c)

Simplifying this expression, we get:

x = [-(2a-b-c) ± √(4a^2 + b^2 + c^2 - 4ab - 4ac + 8bc)] / 2(a b-2c)

x = [-(2a-b-c) ± √((2a - b + 2c)^2 - 4(a + c)(a - 2b))] / 2(a b-2c)

x = [-(2a-b-c) ± √((2a - b + 2c)^2 - 4(a + c)(a - 2b))] / 2(a b-2c)

x = [-(2a-b-c) ± √((2a - b + 2c)^2 - 4(a + c)(a - 2b))] / 2(a b-2c)

Now, we can simplify the discriminant under the square root as follows:

(2a - b + 2c)^2 - 4(a + c)(a - 2b)

= 4a^2 + b^2 + 4c^2 - 4ab - 8ac + 8bc - 4a^2 + 8ab - 16bc

= b^2 + 4c^2 - 4ac - 4bc

= (b - 2c)^2

Substituting this back into the quadratic formula, we get:

x = [-(2a-b-c) ± (b - 2c)] / 2(a b-2c)

x = [-2a+b+c ± (b - 2c)] / 2(a b-2c)

x = (b - 2c) / 2(a b-2c) or x = c / a-2b

Therefore, the solutions of the quadratic equation are:

x = (b - 2c) / 2(a b-2c) or x = c / a-2b

Comparing these solutions with the given options, we can see that the correct answer is option B, x = -1.