Question 738852
{{{sqrt(2x-14) - sqrt(x) + 4 = 3}}}

{{{sqrt(2x-14)-sqrt(2x-14) - sqrt(x) + 4-3 =3-3 -sqrt(2x-14)}}}


{{{1 - sqrt(x)  =-sqrt(2x-14)}}}



squaring...

{{{(1 - sqrt(x) )^2 =(-sqrt(2x-14))^2}}}




rearranging then squaring again...
{{{
1-2sqrt(x)+x=2x-14
}}}



{{{
-2sqrt(x)=x-15
}}}



{{{
(2sqrt(x))^2=(x-15)^2
}}}



{{{
4x=x^2-30x+225
}}}


{{{
x^2-34x+225=0
}}}


{{{(x-9)(x-25)=0}}}


After testing we find that x=25 does not work so our only solution is x=9






:)