What is the answer to 3x=sqrt(3x+7)-1 ?

The answer to 3x=sqrt(3x+7)-1 is x= 2/3

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3x=sqrt(3x+7)-1

3 x = 3 x + 7 - 1

x = \frac{2}{3}

Decimal Notation

x = 0.66666 \dots

Solution steps

3 x = 3 x + 7 - 1

Remove square roots

9 x^{2} + 6 x + 1 = 3 x + 7

Solve

9 x^{2} + 6 x + 1 = 3 x + 7 : x = \frac{2}{3}, x = - 1

x = \frac{2}{3}, x = - 1

Verify Solutions:

x = \frac{2}{3}

True

, x = - 1

False

The solution is

x = \frac{2}{3}

x - 6 x + 8 = 0

x + 3 - 8 x + 1 = - 1

x + 7 - 1 = x - 4

3 x + 1 = 2

x, y - 2 = x + 1