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

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

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

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

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

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} = \frac{2}{3}

Multiply both sides by

3

3 x^{2} + 3 x + 1 = 2

Move

2

to the left side

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}

12 x = 100 x^{2} - 2 \times 9.8 \times 5

- 2 x^{2} - 5 x = 7

s^{2} + 2 s - 6 = 0

3 p (5 p - 1) = 0

6 x^{2} + 17 x = 24 + 7 x

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