Question 204498
square both sides of the equation
{{{sqrt(3x) - sqrt(3x-5) = 1}}}
{{{(sqrt(3x) - sqrt(3x-5))^2 = (1)^2}}}
{{{3x - 2*sqrt(3x*(3x-5)) + 3x - 5 = 1}}}
{{{3x + 3x - 5 - 1 = 2*sqrt(3x*(3x-5))}}}
{{{6x - 6 = 2*sqrt(3x*(3x-5))}}}

square them again:
{{{(6x - 6)^2 = (2*sqrt(3x*(3x-5)))^2}}}
{{{36x^2 - 72x + 36 = 4*3x*(3x-5)}}}
{{{36x^2 - 72x + 36 = 36x^2 - 60x}}}
{{{36x^2 - 72x + 36 - 36x^2 + 60x = 0}}}
{{{-12x + 36 = 0}}}

12x = 36
x = 36/12 = 3