(x-3)²+(x-4)²-(x-5)²-x=24

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To solve this equation, we need to first expand and simplify both sides:

((x-3)² + (x-4)²) - (x-5)² - x = 2
(x² - 6x + 9 + x² - 8x + 16) - (x² - 10x + 25) - x = 2
(2x² - 14x + 25) - x² + 10x - 25 - x = 2
2x² - 14x + 25 - x² + 10x - 25 - x = 2
x² - 5x = 24

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

x² - 5x - 24 = 0

Finally, we can factor the quadratic equation:

(x - 8)(x + 3) = 0

Setting each factor to zero gives us two possible solutions:

x - 8 =
x = 8

x + 3 =
x = -3

Therefore, the solutions to the equation are x = 8 and x = -3.