(2х-9)^2=(4х-3)^3

To solve this equation, we can first expand both sides and simplify the expression.

Expanding the left side: (2x - 9)^2 = (2x - 9)(2x - 9) = 4x^2 - 18x - 18x + 81 = 4x^2 - 36x + 81

Expanding the right side: (4x - 3)^3 = (4x - 3)(4x - 3)(4x - 3) = (16x^2 - 12x - 12x + 9)(4x - 3) = (16x^2 - 24x + 9)(4x - 3) = 64x^3 - 96x^2 + 36x - 48x^2 + 72x - 27 = 64x^3 - 144x^2 + 108x - 27

Now, we can set the expanded expressions equal to each other: 4x^2 - 36x + 81 = 64x^3 - 144x^2 + 108x - 27

Rearranging the terms and simplifying: 64x^3 - 144x^2 + 108x - 27 - 4x^2 + 36x - 81 = 0 64x^3 - 148x^2 + 144x - 108 = 0

Unfortunately, this equation cannot be easily solved by traditional methods. You may need to use numerical methods or a graphing calculator to find an approximate solution.