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

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

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

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

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

x = - \frac{1}{3} + i \frac{2}{3}, x = - \frac{1}{3} - i \frac{2}{3}

Solution steps

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

Multiply both sides by

3

3 x^{2} + 2 x + 1 = 0

Solve with the quadratic formula

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

Simplify

2^{2} - 4 \cdot 3 \cdot 1 : 22 i

x_{1, 2} = \frac{- 2 \pm 2 2 i}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- 2 + 2 2 i}{2 \cdot 3}, x_{2} = \frac{- 2 - 2 2 i}{2 \cdot 3}

x = \frac{- 2 + 2 2 i}{2 \cdot 3} : - \frac{1}{3} + i \frac{2}{3}

x = \frac{- 2 - 2 2 i}{2 \cdot 3} : - \frac{1}{3} - i \frac{2}{3}

The solutions to the quadratic equation are:

x = - \frac{1}{3} + i \frac{2}{3}, x = - \frac{1}{3} - i \frac{2}{3}

- 5 x^{2} + 20 x - 15 = 0

15 x^{2} - 29 x + 8 = - 4

1.25 x^{2} = 15 x

12 x^{2} - 312 x + 1512 = 0

x, 4 x^{2} + 6 y^{2} - z^{2} = - 5

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