What are the solutions to the equation 3x(x-2)=x-6 ?

The solutions to the equation 3x(x-2)=x-6 are x= 7/6+i(sqrt(23))/6 ,x= 7/6-i(sqrt(23))/6

Find the zeros of 3x(x-2)=x-6

The zeros of 3x(x-2)=x-6 are x= 7/6+i(sqrt(23))/6 ,x= 7/6-i(sqrt(23))/6

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3 x (x - 2) = x - 6

x = \frac{7}{6} + i \frac{23}{6}, x = \frac{7}{6} - i \frac{23}{6}

Solution steps

3 x (x - 2) = x - 6

Expand

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

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

Move

6

to the left side

3 x^{2} - 6 x + 6 = x

Move

x

to the left side

3 x^{2} - 7 x + 6 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot 3 \cdot 6}{2 \cdot 3}

Simplify

(- 7)^{2} - 4 \cdot 3 \cdot 6 : 23 i

x_{1, 2} = \frac{- ( - 7 ) \pm 23 i}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 7 ) + 23 i}{2 \cdot 3}, x_{2} = \frac{- ( - 7 ) - 23 i}{2 \cdot 3}

x = \frac{- ( - 7 ) + 23 i}{2 \cdot 3} : \frac{7}{6} + i \frac{23}{6}

x = \frac{- ( - 7 ) - 23 i}{2 \cdot 3} : \frac{7}{6} - i \frac{23}{6}

The solutions to the quadratic equation are:

x = \frac{7}{6} + i \frac{23}{6}, x = \frac{7}{6} - i \frac{23}{6}

\frac{1}{2} b + 1 = 3

\frac{x ^{2} - 6}{2} - \frac{x ^{2} + 4}{4} = 5

- 0.3 x - 7.2 \leq 0.1 x + 0.4

x^{4} - 10 x + 9

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What are the solutions to the equation 3x(x-2)=x-6 ?
The solutions to the equation 3x(x-2)=x-6 are x= 7/6+i(sqrt(23))/6 ,x= 7/6-i(sqrt(23))/6
Find the zeros of 3x(x-2)=x-6
The zeros of 3x(x-2)=x-6 are x= 7/6+i(sqrt(23))/6 ,x= 7/6-i(sqrt(23))/6