What are the solutions to the equation 6x(x-5)=x-5 ?

The solutions to the equation 6x(x-5)=x-5 are x=5,x= 1/6

Find the zeros of 6x(x-5)=x-5

The zeros of 6x(x-5)=x-5 are x=5,x= 1/6

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6 x (x - 5) = x - 5

x = 5, x = \frac{1}{6}

Decimal Notation

x = 5, x = 0.16666 \dots

Solution steps

6 x (x - 5) = x - 5

Expand

6 x (x - 5) : 6 x^{2} - 30 x

6 x^{2} - 30 x = x - 5

Move

5

to the left side

6 x^{2} - 30 x + 5 = x

Move

x

to the left side

6 x^{2} - 31 x + 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 31 ) \pm ( - 31 ) ^{2} - 4 \cdot 6 \cdot 5}{2 \cdot 6}

(- 31)^{2} - 4 \cdot 6 \cdot 5 = 29

x_{1, 2} = \frac{- ( - 31 ) \pm 29}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- ( - 31 ) + 29}{2 \cdot 6}, x_{2} = \frac{- ( - 31 ) - 29}{2 \cdot 6}

x = \frac{- ( - 31 ) + 29}{2 \cdot 6} : 5

x = \frac{- ( - 31 ) - 29}{2 \cdot 6} : \frac{1}{6}

The solutions to the quadratic equation are:

x = 5, x = \frac{1}{6}

4.9 x^{2} + 16.8 x + 7.6 = 0

- 4 = x^{2} + 5 x

x^{2} + 10 x = - 9

4 k^{2} - 2 = - 15

22 - 22 x = (5 x + 3) (x - 1)

What are the solutions to the equation 6x(x-5)=x-5 ?
The solutions to the equation 6x(x-5)=x-5 are x=5,x= 1/6
Find the zeros of 6x(x-5)=x-5
The zeros of 6x(x-5)=x-5 are x=5,x= 1/6