<PRE><B>Question 938345</B>
the square root of three times a certain number is subtracted from the number and the result is 6 .
{{{x - sqrt(3x) = 6}}}
We can arrange it like this
x - 6 = {{{sqrt(3x)}}}
square both sides
(x-6)^2 = 3x
x^2 - 12x + 36 = 3x
x^2 - 12x - 3x + 36 = 0
x^2 - 15x + 36 = 0
Factors to
(x-12)(x-3) = 0
Two solutions
x = 12
x = 3
:
Check both solutions in the original equation
{{{12 - sqrt(3*12) = 6}}}
12 - 6 = 6, a good solution
and
{{{3 - sqrt(3*3) = 6}}}
3 - 3 does not  = 6, no solution
: 
find the number x = 12</PRE>