Answer:
3
Step-by-step explanation:
[tex]x=\sqrt{2x+3}[/tex]
square both sides: [tex]x^2=2x+3[/tex]
subtract [tex]2x + 3[/tex] from both sides: [tex]x^2-2x-3=0[/tex]
factorize: [tex](x-3)(x+1)[/tex]
Therefore, [tex]x=3 \ and \ -1[/tex]
Substitute found values of [tex]x[/tex] back into original equation:
[tex]3=\sqrt{2\times3+3}=3 \ \ \checkmark[/tex]
[tex]-1=\sqrt{2\times-1+3}=1[/tex] incorrect!
So answer is [tex]x = 3[/tex] only
