What are the solutions to the equation 6x(1-x)=x ?

The solutions to the equation 6x(1-x)=x are x=0,x= 5/6

Find the zeros of 6x(1-x)=x

The zeros of 6x(1-x)=x are x=0,x= 5/6

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6 x (1 - x) = x

x = 0, x = \frac{5}{6}

Decimal Notation

x = 0, x = 0.83333 \dots

Solution steps

6 x (1 - x) = x

Expand

6 x (1 - x) : 6 x - 6 x^{2}

6 x - 6 x^{2} = x

Move

x

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 ( - 6 ) \cdot 0}{2 ( - 6 )}

5^{2} - 4 (- 6) \cdot 0 = 5

x_{1, 2} = \frac{- 5 \pm 5}{2 ( - 6 )}

Separate the solutions

x_{1} = \frac{- 5 + 5}{2 ( - 6 )}, x_{2} = \frac{- 5 - 5}{2 ( - 6 )}

x = \frac{- 5 + 5}{2 ( - 6 )} : 0

x = \frac{- 5 - 5}{2 ( - 6 )} : \frac{5}{6}

The solutions to the quadratic equation are:

x = 0, x = \frac{5}{6}

- 16 x^{2} + 240 x + 180 = 0

9 x^{2} - 30 x - 25 = 0

9 x^{2} - 8 x = 0

4 x^{2} + 8 x + 80 = 0

(2 D - 1)^{2} = 0

What are the solutions to the equation 6x(1-x)=x ?
The solutions to the equation 6x(1-x)=x are x=0,x= 5/6
Find the zeros of 6x(1-x)=x
The zeros of 6x(1-x)=x are x=0,x= 5/6