First note that [tex]x\ge0[/tex]; otherwise [tex]\sqrt{2x}[/tex] is undefined as long as we're only looking for real solutions.
We can write
[tex]\sqrt{2x}+12=x+8[/tex]
[tex]\sqrt{2x}=x-4[/tex]
[tex]2x=(x-4)^2[/tex]
[tex]2x=x^2-8x+16[/tex]
[tex]x^2-10x+16=0[/tex]
[tex](x-8)(x-2)=0[/tex]
[tex]\implies x=8,x=2[/tex]
