Question 192330
3+sq  rt  (5x-1) =  x

subt  3  each  side

sq rt(5x-1) = x-3

sq  both  sides

+-(5x-1) = (X-3)^2 

USING  ONLY +  answer  (  -  answer  gives  imaginary  answers)

+(5x-1) = (x-3)(x-3)= x^2-6x+9

subt  5x  each  side

-1 = x^2 -6x +9 -5x

add  1  to  each  side

0= X^2 -6x +9 -5x +1
simplifying

0=x^2 -11x +10

factoring
0=(x-10)(x-1)
x=10  and  x=1
checking
3 +sq rt (5x-1) = x
3 + sq rt (5(1)-1) = (1)
3 + sqrt 4=1
3+-2 =1      ok  with  -2

for  x=10
3+sqrt (5(10)-1) = (10)
3+ sqrt 49 =10
3+-7=10   ok  with  +7