What are the solutions to the equation 3x^2-6x-1=0 ?

The solutions to the equation 3x^2-6x-1=0 are x=(3+2sqrt(3))/3 ,x=(3-2sqrt(3))/3

Find the zeros of 3x^2-6x-1=0

The zeros of 3x^2-6x-1=0 are x=(3+2sqrt(3))/3 ,x=(3-2sqrt(3))/3

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

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

Decimal Notation

x = 2.15470 \dots, x = - 0.15470 \dots

Solution steps

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

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 3 ( - 1 )}{2 \cdot 3}

(- 6)^{2} - 4 \cdot 3 (- 1) = 43

x_{1, 2} = \frac{- ( - 6 ) \pm 4 3}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 4 3}{2 \cdot 3}, x_{2} = \frac{- ( - 6 ) - 4 3}{2 \cdot 3}

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

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

The solutions to the quadratic equation are:

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

24 p^{6} q + 42 p^{5} q^{4} + 54 p^{2} q^{2}

\frac{3 + 2 i}{2 - 3 i}

x^{3} + 5 x^{2}

(w + 5) (w - 3) = (w + 6) (w + 4)

\frac{1}{2} x - 3 = 10

What are the solutions to the equation 3x^2-6x-1=0 ?
The solutions to the equation 3x^2-6x-1=0 are x=(3+2sqrt(3))/3 ,x=(3-2sqrt(3))/3
Find the zeros of 3x^2-6x-1=0
The zeros of 3x^2-6x-1=0 are x=(3+2sqrt(3))/3 ,x=(3-2sqrt(3))/3