[tex]\sf \sqrt{x^2+2x-3}=2 \sqrt{3} \\
\sqrt{x^2-x+3x-3}=2 \sqrt{3} \\
\sqrt{x(x-1)+3(x-1)}=2 \sqrt{3} \\
\sqrt{(x+3)(x-1)}=2 \sqrt{3} \\
\sqrt{(x+3)(x-1)}= \sqrt{12} \\
(x+3)(x-1)=12 \\
x+3=6 \longrightarrow x=3 \\
x-1=2 \longrightarrow x=3 \\ \\
\boxed{ \sf Singura~varianta:x=3}[/tex]
