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

The solutions to the equation 3x^2-3x-1=0 are x=(3+sqrt(21))/6 ,x=(3-sqrt(21))/6

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

The zeros of 3x^2-3x-1=0 are x=(3+sqrt(21))/6 ,x=(3-sqrt(21))/6

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

x = \frac{3 + 21}{6}, x = \frac{3 - 21}{6}

Decimal Notation

x = 1.26376 \dots, x = - 0.26376 \dots

Solution steps

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

Solve with the quadratic formula

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

(- 3)^{2} - 4 \cdot 3 (- 1) = 21

x_{1, 2} = \frac{- ( - 3 ) \pm 21}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 21}{2 \cdot 3}, x_{2} = \frac{- ( - 3 ) - 21}{2 \cdot 3}

x = \frac{- ( - 3 ) + 21}{2 \cdot 3} : \frac{3 + 21}{6}

x = \frac{- ( - 3 ) - 21}{2 \cdot 3} : \frac{3 - 21}{6}

The solutions to the quadratic equation are:

x = \frac{3 + 21}{6}, x = \frac{3 - 21}{6}

8 - 3 Y \leq 8

\frac{3}{2} + 1

(6 x)^{2}

\frac{3}{4} + \frac{2}{5}

554

What are the solutions to the equation 3x^2-3x-1=0 ?
The solutions to the equation 3x^2-3x-1=0 are x=(3+sqrt(21))/6 ,x=(3-sqrt(21))/6
Find the zeros of 3x^2-3x-1=0
The zeros of 3x^2-3x-1=0 are x=(3+sqrt(21))/6 ,x=(3-sqrt(21))/6