What are the solutions to the equation 3x(x-2)=9x^2-7x ?

The solutions to the equation 3x(x-2)=9x^2-7x are x=0,x= 1/6

Find the zeros of 3x(x-2)=9x^2-7x

The zeros of 3x(x-2)=9x^2-7x are x=0,x= 1/6

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3 x (x - 2) = 9 x^{2} - 7 x

x = 0, x = \frac{1}{6}

Decimal Notation

x = 0, x = 0.16666 \dots

Solution steps

3 x (x - 2) = 9 x^{2} - 7 x

Expand

3 x (x - 2) : 3 x^{2} - 6 x

3 x^{2} - 6 x = 9 x^{2} - 7 x

Move

7 x

to the left side

3 x^{2} + x = 9 x^{2}

Move

9 x^{2}

to the left side

- 6 x^{2} + x = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 ( - 6 ) \cdot 0}{2 ( - 6 )}

1^{2} - 4 (- 6) \cdot 0 = 1

x_{1, 2} = \frac{- 1 \pm 1}{2 ( - 6 )}

Separate the solutions

x_{1} = \frac{- 1 + 1}{2 ( - 6 )}, x_{2} = \frac{- 1 - 1}{2 ( - 6 )}

x = \frac{- 1 + 1}{2 ( - 6 )} : 0

x = \frac{- 1 - 1}{2 ( - 6 )} : \frac{1}{6}

The solutions to the quadratic equation are:

x = 0, x = \frac{1}{6}

16 x = x^{2}

4 (x - 3)^{2} = 144

- x^{2} + 3 x + 3 = 0

0 = 5 x^{2} - 4

x^{2} - 10 x + 20

What are the solutions to the equation 3x(x-2)=9x^2-7x ?
The solutions to the equation 3x(x-2)=9x^2-7x are x=0,x= 1/6
Find the zeros of 3x(x-2)=9x^2-7x
The zeros of 3x(x-2)=9x^2-7x are x=0,x= 1/6