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}

Solution steps

9 x^{2} = 3 x + 1

Move

1

to the left side

9 x^{2} - 1 = 3 x

Move

3 x

to the left side

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

Write in the standard form

a x^{2} + b x + c = 0

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}

a^{2} + 3 a - 40

(x - 2) (x - 4) = 0

8 x^{5} y^{3} + 32 x^{2} y^{8} - 64 x^{4} y^{2}

x (x + 2) = 5 (x + x + 2) - 1

π \cdot 3^{2}

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