(5х-1)(2-х)=(х-3)(2-5х)

To solve this equation, we can start by simplifying both sides:

(5x-1)(2-x) = (x-3)(2-5x)

Expanding both sides of the equation:

10x - 2x^2 - 2 + x = 2x - 6 - 5x^2 + 15x

Rearranging terms in descending powers of x:

-2x^2 + 11x - 2 = -5x^2 + 17x - 6

Next, we can bring all the terms to one side to set the equation equal to zero:

-2x^2 + 11x - 2 + 5x^2 - 17x + 6 = 0

Combining like terms:

3x^2 - 6x + 4 = 0

This is a quadratic equation. To solve for x, we can either factor the quadratic or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b^2-4ac)) / (2a)

Where a = 3, b = -6, and c = 4.

x = (-(-6) ± √((-6)^2 - 4(3)(4))) / (2(3))

Simplifying:

x = (6 ± √(36 - 48)) / 6

x = (6 ± √(-12)) / 6

Since we have a negative value under the square root, the equation has no real solutions.