Solve for x.
(x-1)/(x-3)=sqrt of 17-x
(x-1)/(x-3) = √(17-x)
(x-1)^2/(x-3)^2 = (17-x)
x^2-2x+1 = -x^3+23x^2-111x+153
x^3-22x^2+109x-152 = 0
No rational roots here, so you will need to resort to a graphical or numeric method to get the desired accuracy.
http://www.wolframalpha.com/input/?i=x^3-22x^2%2B109x-152