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

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

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

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

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

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

Solution steps

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

Switch sides

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}

12 x^{2} - x - 6

4 x^{3} + 20 x^{2} - 9 x - 45

- 2 = 2 x^{2} + 8

2 k^{2} + 11 k + 15

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