What are the solutions to the equation 3x^2-2sqrt(3)x-1=0 ?

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

Find the zeros of 3x^2-2sqrt(3)x-1=0

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

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3 x^{2} - 23 x - 1 = 0

x = \frac{3 + 6}{3}, x = \frac{3 - 6}{3}

Decimal Notation

x = 1.39384 \dots, x = - 0.23914 \dots

Solution steps

3 x^{2} - 23 x - 1 = 0

Solve with the quadratic formula

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

(- 23)^{2} - 4 \cdot 3 (- 1) = 26

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = \frac{3 + 6}{3}, x = \frac{3 - 6}{3}

49 x^{2} = 81

100 x^{2} = 64

\frac{10 x + 1}{2} = \frac{9}{2}

x + \frac{1}{3} (x - 3 - \frac{1}{2} (4 - 3 x)) = \frac{2}{3} (1 - \frac{5 x}{2})

\frac{3}{3 15}

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