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

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

Find the zeros of 9x^2+3x=1

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

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9 x^{2} + 3 x = 1

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

Decimal Notation

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

Solution steps

9 x^{2} + 3 x = 1

Move

1

to the left side

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}

100 x^{2} - 20 x + 1

2 a y^{2} + 5 a y - 3 a

\frac{1}{18} w - \frac{1}{36} + \frac{1}{3} w = \frac{1}{3} + w

- (- 4)^{2}

64 b^{2} = 9

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