2x^2-6x+3/2
= 2(x^2-3x+3/4)
= 2{(x^2-3x+9/4)-9/4+3/4}
= 2{(x^2-3x+9/4)-6/4}
= 2{(x-3/2)^2-(√6/2)^2}
= 2(x-3/2+√6/2)(x-3/2-√6/2)
2x^2-6x+3/2
= 2(x^2-3x+3/4)
= 2{(x^2-3x+9/4)-9/4+3/4}
= 2{(x^2-3x+9/4)-6/4}
= 2{(x-3/2)^2-(√6/2)^2}
= 2(x-3/2+√6/2)(x-3/2-√6/2)