Question

x-sqrt{x+3}=x/2

Answer 1

Rewrite the equation as
\(x-(x/2)=\sqrt{x+3}\)
\(x/2=\sqrt{x+3}\)
Square both sides
\(x^2/4=x+3\)
\(x^2=4x+12\)
\(x^2-4x-12=0\)
\((x-6)(x+2)=0\)
\(x=6\) or \(x=-2\)
After inspection \(x=-2\) doesn't work. So \(x=6\) is the only solution!