What are the solutions to the equation x(3x-1)= 1/2 ?

The solutions to the equation x(3x-1)= 1/2 are x=(1+sqrt(7))/6 ,x=(1-sqrt(7))/6

Find the zeros of x(3x-1)= 1/2

The zeros of x(3x-1)= 1/2 are x=(1+sqrt(7))/6 ,x=(1-sqrt(7))/6

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x (3 x - 1) = \frac{1}{2}

x = \frac{1 + 7}{6}, x = \frac{1 - 7}{6}

Decimal Notation

x = 0.60762 \dots, x = - 0.27429 \dots

Solution steps

x (3 x - 1) = \frac{1}{2}

Multiply both sides by

2

2 x (3 x - 1) = 1

Expand

2 x (3 x - 1) : 6 x^{2} - 2 x

6 x^{2} - 2 x = 1

Move

1

to the left side

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

Solve with the quadratic formula

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

(- 2)^{2} - 4 \cdot 6 (- 1) = 27

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

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2 7}{2 \cdot 6}, x_{2} = \frac{- ( - 2 ) - 2 7}{2 \cdot 6}

x = \frac{- ( - 2 ) + 2 7}{2 \cdot 6} : \frac{1 + 7}{6}

x = \frac{- ( - 2 ) - 2 7}{2 \cdot 6} : \frac{1 - 7}{6}

The solutions to the quadratic equation are:

x = \frac{1 + 7}{6}, x = \frac{1 - 7}{6}

a^{2} + 8 a + 15 = 0

- 35 = 16 x - 3 x^{2}

7 x^{2} - 7 x - 6 = 6 x^{2} - x + 1

x^{2} - 4 \times + 4 = 0

6 x - 2 x^{2} = 0

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