What are the solutions to the equation x(6-4x)=1 ?

The solutions to the equation x(6-4x)=1 are x=(3-sqrt(5))/4 ,x=(3+sqrt(5))/4

Find the zeros of x(6-4x)=1

The zeros of x(6-4x)=1 are x=(3-sqrt(5))/4 ,x=(3+sqrt(5))/4

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x (6 - 4 x) = 1

x = \frac{3 - 5}{4}, x = \frac{3 + 5}{4}

Decimal Notation

x = 0.19098 \dots, x = 1.30901 \dots

Solution steps

x (6 - 4 x) = 1

Expand

x (6 - 4 x) : 6 x - 4 x^{2}

6 x - 4 x^{2} = 1

Move

1

to the left side

6 x - 4 x^{2} - 1 = 0

Write in the standard form

a x^{2} + b x + c = 0

- 4 x^{2} + 6 x - 1 = 0

Solve with the quadratic formula

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

6^{2} - 4 (- 4) (- 1) = 25

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

Separate the solutions

x_{1} = \frac{- 6 + 2 5}{2 ( - 4 )}, x_{2} = \frac{- 6 - 2 5}{2 ( - 4 )}

x = \frac{- 6 + 2 5}{2 ( - 4 )} : \frac{3 - 5}{4}

x = \frac{- 6 - 2 5}{2 ( - 4 )} : \frac{3 + 5}{4}

The solutions to the quadratic equation are:

x = \frac{3 - 5}{4}, x = \frac{3 + 5}{4}

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

3 x - 4 = 2 x + 0.7

9 x^{2} y + 6 x y - 12 x

2 x (x - 3) = x - 3

What are the solutions to the equation x(6-4x)=1 ?
The solutions to the equation x(6-4x)=1 are x=(3-sqrt(5))/4 ,x=(3+sqrt(5))/4
Find the zeros of x(6-4x)=1
The zeros of x(6-4x)=1 are x=(3-sqrt(5))/4 ,x=(3+sqrt(5))/4