Verified Answer :

anijlin

\(\sqrt{6x-9} = x\)

first we are going to get rid of the square root by raising both sides to the power of 2

6x - 9 = x²
x² - 6x + 9 = 0

now the equation is a quadratic, and you can solve for x 

i'm going to factor it, but there are many ways to solve for a quadratic
(x - 3)(x - 3) = 0
If you FOIL this, it becomes x² - 6x + 9 

(x - 3)² = 0
x - 3 = 0
x = 3

to check the answer, you can plug 3 back into the original equation

\(\sqrt{6(3) - 9} = 3\)
\(\sqrt{18 - 9} = 3\)
\(\sqrt{9} = 3\)
\(3 = 3\)

√6x-9=x
6x-9=x²
x²-6x+9=0
(x-3)(x-3)=0
x=3
check
√6*3-9=3
√18-9=3
√9=3
3=3

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