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

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

Find the zeros of roots 3x^2-4x-1

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

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roots

3 x^{2} - 4 x - 1

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

Solution steps

3 x^{2} - 4 x - 1

The roots are the intercepts with the x-axis

(y = 0)

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}

9 x^{2} - 1 = 35

2 x^{2} - 8 = - 17

3 u^{2} + 6 = - 11 u

k^{2} + 10 k + 15 = 0

m^{2} + 4

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