`x^2+4x+18=6\sqrt{x+5} + 2x\sqrt{3x+4}` (đk: `x>= -4/3`)

`<=> (36(x+5) - 324)/(6\sqrt{x+5}+18) + (4x^2(3x+4) - 1024)/(2x\sqrt{3x+4} + 32) - x^2-4x+32=0`

`<=> (36x+180-324)/(6\sqrt{x+5}+18) + (12x^3+16x^2-1024)/(2x\sqrt{3x+4} + 32)-x^2-4x+32=0`

`<=> (36x-144)/(6\sqrt{x+5}+18) + (12x^3-48x^2+64x^2-1024)/(2x\sqrt{3x+4} + 32) - x^2-4x+32=0`

`<=> (36x-144)/(6\sqrt{x+5}+18) + (12x^2(x-4)+(8x)^2-32^2)/(2x\sqrt{3x+4} + 32) - x^2-4x+32=0`

`<=> (36x-144)/(6\sqrt{x+5}+18) + (12x^2(x-4)+(8x-32)(8x+32))/(2x\sqrt{3x+4} + 32) - x^2-4x+32=0`

`<=> (36x-144)/(6\sqrt{x+5}+18) + (12x^2(x-4)+8(x-4)(8x+32))/(2x\sqrt{3x+4} + 32) - x^2-4x+32=0`

`<=> (36(x-4))/(6\sqrt{x+5}+18) + ((x-4)(12x^2+64x+256))/(2x\sqrt{3x+4} + 32) -(x-4)(x+8)=0`

`<=> (x-4)( 36/(6\sqrt{x+5}+18) + (12x^2+64x+256)/(2x\sqrt{3x+4} + 32) - x-8)=0`

Mà `x>=-4/3=> 36/(6\sqrt{x+5}+18) + (12x^2+64x+256)/(2x\sqrt{3x+4} + 32) - x-8 \ne0`

`=> x-4=0`

`<=> x=4(tm)`

Thử lại TM

Vậy `S={4}`