\(\displaystyle sqrt(x-3)+1=x\)

\(\displaystyle sqrt(x-3)=x-1\)

\(\displaystyle (sqrt(x-3))^2=(x-1)^2\)

\(\displaystyle x-3=(x-1)(x-1)\)

\(\displaystyle x-3=x^2-x-x-1\)

\(\displaystyle x-3=x^2-2x+1\)

\(\displaystyle 0=x^2-3x+4\)

I need an actual number so I can check the solution.