Question 967069
Personally and as typically taught, first isolate the one radical...

This can be started in ones head:
{{{sqrt(17-4x)=x-3}}}


Now square both sides:
{{{17-4x=x^2-6x+3}}}


...into general form:
{{{x^2-2x+3-17}}}
{{{x^2-2x-14=0}}}
-
{{{x=(2+- sqrt(4+4*14))/2}}}
{{{x=(2+- sqrt(60))/2}}}
{{{x=(2+- 2sqrt(15))/2}}}
{{{highlight(x=1+- sqrt(15))}}}



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Step #2 in the originally given problem looks very bad.