2x^{2} - 5x + 3 = 0

2x^{2}/2 - 5x/2 + 3/2 = 0 (dividing both sides by 2)

x^{2} - 5x/2 + 3/2 = 0

[x^{2} - 5x/2 + (5/4)^{2}] - (5/4)^{2} + 3/2 = 0

[x - 5/4]^{2} - 25/16 + 3/2 = 0

[x - 5/4]^{2} - (25-24)/16 = 0

[x - 5/4]^{2} - 1/16 = 0

[x - 5/4]^{2} = 1/16

x - 5/4 = *± *1/4 (square rooting on both sides)

x = 1/4 + 5/4 or x = -1/4 + 5/4

x = (1+5)/4 or x = (-1+5)/4

x = 6/4 or x = 4/4

x = 3/2 or x = 1