What are the solutions to the equation 9x^2-3x-1=0 ?

The solutions to the equation 9x^2-3x-1=0 are x=(1+sqrt(5))/6 ,x=(1-sqrt(5))/6

Find the zeros of 9x^2-3x-1=0

The zeros of 9x^2-3x-1=0 are x=(1+sqrt(5))/6 ,x=(1-sqrt(5))/6

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

x = \frac{1 + 5}{6}, x = \frac{1 - 5}{6}

Decimal Notation

x = 0.53934 \dots, x = - 0.20601 \dots

Solution steps

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

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 9 ( - 1 )}{2 \cdot 9}

(- 3)^{2} - 4 \cdot 9 (- 1) = 35

x_{1, 2} = \frac{- ( - 3 ) \pm 3 5}{2 \cdot 9}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 3 5}{2 \cdot 9}, x_{2} = \frac{- ( - 3 ) - 3 5}{2 \cdot 9}

x = \frac{- ( - 3 ) + 3 5}{2 \cdot 9} : \frac{1 + 5}{6}

x = \frac{- ( - 3 ) - 3 5}{2 \cdot 9} : \frac{1 - 5}{6}

The solutions to the quadratic equation are:

x = \frac{1 + 5}{6}, x = \frac{1 - 5}{6}

x - 1 + 2 x - 1 = - 5

2 w^{2} + 3 w - 77

2 x = 9 - x^{2}

882 = - 13.957 x^{2} + 310.63 x + 31.971

x y^{2} - y^{3}

What are the solutions to the equation 9x^2-3x-1=0 ?
The solutions to the equation 9x^2-3x-1=0 are x=(1+sqrt(5))/6 ,x=(1-sqrt(5))/6
Find the zeros of 9x^2-3x-1=0
The zeros of 9x^2-3x-1=0 are x=(1+sqrt(5))/6 ,x=(1-sqrt(5))/6