Question 611
Well, first we need to get rid of the sqare root. To do this, we need to get it on its own:

{{{sqrt(7x-3)=2x-3}}}

Then square both sides:

{{{7x-3=(2x-3)^2}}}

Expand the brackets:

{{{7x-3=4x^2 -12x +9}}}

Get everything on one side:

{{{4x^2-19x+12=0}}}

In this case, the easiest way to solve it is to use the quadratic equation:

{{{x = (19 +- sqrt( (-19)^2-4*4*12 ))/(2*4) }}}

{{{x = (19 +- sqrt( 361 - 192 ))/8}}}

{{{x = (19 +- 13)/8}}}

{{{x = 32/8,6/8}}}

{{{x = 4,3/4}}}