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

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

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

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

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x^{2} + x - \frac{1}{3} = 0

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

Decimal Notation

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

Solution steps

x^{2} + x - \frac{1}{3} = 0

Multiply both sides by

3

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}

x^{2} - 4 = 2 x - 1

4 x^{2} + 24 x - 4 = 0

x + 1 = x (x - 2)

4 m^{2} + 96 = - 40 m

v^{2} + 3 v - 18 = 0

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