$#DAnh$

`a.`

`(x+2)^2 - (x-3)(x-5) = 18`

`(x^2+4x+4)-(x^2-5x-3x+15) = 18`

`x^2+4x+4-x^2+5x+3x-15 - 18 = 0`

`12x - 29 = 0`

`12x = 29`

`x = 29/12`

Vậy `x = 29/12`

`b.`

`(4x+2)(9x-5)-(6x-3)^2 = 12`

`(36x^2-20x+18x-10)-(36x^2 - 36x+9) = 12`

`36x^2-20x+18x-10-36x^2+ 36x-9 = 12`

`36x^2-20x+18x-10-36x^2+ 36x-9 - 12 = 0`

`34x -31 = 0`

`34x = 31`

`x = 31/34`

Vậy `x = 31/34`

`c.`

`(x-8)^2 - (3x+2)(3x-2) = 15`

`(x^2-16x+64)-[(3x)^2-2^2] = 15`

`(x^2-16x+64)-(9x^2-4) =15`

`x^2-16x+64-9x^2+4 =15`

`x^2-16x+64-9x^2+4-15 = 0`

`-8x^2 - 16x + 53 = 0`

`8x^2 + 16x - 53 = 0`

`Delta = 16^2 - 4. 8. (-53) = 1952`

`sqrt{Delta} = sqrt{1952} = 4sqrt{122}`

`x_1 = (-16+4sqrt{122})/(2.8) = (-16+4sqrt{122})/16 = (-4+sqrt{122})/4`

`x_2 = (-16-4sqrt{122})/(2.8) = (-16-4sqrt{122})/16 = (-4-sqrt{122})/4`

Vậy `x = (-4+-sqrt{122})/4`

`d.`

`x^2 - 3x + 1 = x - 3`

`x^2 - 3x + 1 - x + 3 = 0`

`x^2 - 4x + 4 = 0`

`(x-2)^2 = 0`

`x-2 = 0`

`x = 2`

Vậy `x = 2`

`e.`

`x^2 - 4x + 7 = 2x + 3`

`x^2 - 4x + 7 - 2x - 3 = 0`

`x^2 -6x + 4 = 0`

`Delta = (-6)^2 - 4. 1. 4 = 20`

`sqrt{Delta} = sqrt{20} = 2sqrt{5}`

`x_1 = (6+2sqrt{5})/2 = 3 + sqrt{5}`

`x_2 = (6-2sqrt{5})/2 = 3 - sqrt{5}`

Vậy `x = 3 +- sqrt{5}`