Expanding both sides of the equation:

Left side:
(2x - 1.5 + 3x + 0.75)^2
(5x + 0.25)^2
(5x + 0.25)(5x + 0.25)
(25x^2 + 1.25x + 1.25x + 0.0625)
25x^2 + 2.5x + 0.0625

Right side:
(3 - x + 1.6667)^2
(3 - x + 5/3)^2
(2 - x)^2
(2 - x)(2 - x)
4 - 2x - 2x + x^2
4 - 4x + x^2

Equating the left and right side of the equation:
25x^2 + 2.5x + 0.0625 = 4 - 4x + x^2

Rearranging the terms:
25x^2 - x^2 + 2.5x + 4x + 0.0625 - 4 = 0
24x^2 + 6.5x - 3.9375 = 0

This is a quadratic equation that can be solved further using quadratic formula:

x = [-b ± √(b^2 - 4ac)] / 2a

where a = 24, b = 6.5, and c = -3.9375

x = [-6.5 ± √(6.5^2 - 424(-3.9375))] / 2*24
x = [-6.5 ± √(42.25 + 379.2)] / 48
x = [-6.5 ± √421.45] / 48

Therefore, the solutions for x in the equation (2x-3/2+3x+3/4)^2 = (3-x+5/3)^2 are:

x = [-6.5 + √421.45] / 48
x = [-6.5 - √421.45] / 48