What are the solutions to the equation 3x^2-4x-1=0 ?

The solutions to the equation 3x^2-4x-1=0 are x=(2+sqrt(7))/3 ,x=(2-sqrt(7))/3

Find the zeros of 3x^2-4x-1=0

The zeros of 3x^2-4x-1=0 are x=(2+sqrt(7))/3 ,x=(2-sqrt(7))/3

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

x = \frac{2 + 7}{3}, x = \frac{2 - 7}{3}

Decimal Notation

x = 1.54858 \dots, x = - 0.21525 \dots

Solution steps

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

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 3 (- 1) = 27

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

Separate the solutions

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

x = \frac{- ( - 4 ) + 2 7}{2 \cdot 3} : \frac{2 + 7}{3}

x = \frac{- ( - 4 ) - 2 7}{2 \cdot 3} : \frac{2 - 7}{3}

The solutions to the quadratic equation are:

x = \frac{2 + 7}{3}, x = \frac{2 - 7}{3}

- 3 (1 - 4 x) + 4 (1 - 2 x) = 4 x + 1

3 u + 5 \geq 11

(5 x)^{\frac{1}{3}}

\frac{3 ( x + 5 )}{4} + \frac{- 7 ( x + 3 )}{10} = 4

4 x - 26 = 5 (2 - x)

What are the solutions to the equation 3x^2-4x-1=0 ?
The solutions to the equation 3x^2-4x-1=0 are x=(2+sqrt(7))/3 ,x=(2-sqrt(7))/3
Find the zeros of 3x^2-4x-1=0
The zeros of 3x^2-4x-1=0 are x=(2+sqrt(7))/3 ,x=(2-sqrt(7))/3