What are the solutions to the equation 6x^2+3=-2x ?

The solutions to the equation 6x^2+3=-2x are x=-1/6+i(sqrt(17))/6 ,x=-1/6-i(sqrt(17))/6

Find the zeros of 6x^2+3=-2x

The zeros of 6x^2+3=-2x are x=-1/6+i(sqrt(17))/6 ,x=-1/6-i(sqrt(17))/6

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6 x^{2} + 3 = - 2 x

x = - \frac{1}{6} + i \frac{17}{6}, x = - \frac{1}{6} - i \frac{17}{6}

Solution steps

6 x^{2} + 3 = - 2 x

Move

2 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 6 \cdot 3}{2 \cdot 6}

Simplify

2^{2} - 4 \cdot 6 \cdot 3 : 217 i

x_{1, 2} = \frac{- 2 \pm 2 17 i}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- 2 + 2 17 i}{2 \cdot 6}, x_{2} = \frac{- 2 - 2 17 i}{2 \cdot 6}

x = \frac{- 2 + 2 17 i}{2 \cdot 6} : - \frac{1}{6} + i \frac{17}{6}

x = \frac{- 2 - 2 17 i}{2 \cdot 6} : - \frac{1}{6} - i \frac{17}{6}

The solutions to the quadratic equation are:

x = - \frac{1}{6} + i \frac{17}{6}, x = - \frac{1}{6} - i \frac{17}{6}

8 x^{2} - 4 x + 6 = 0

4 x^{2} + 12 x - 27 = 13

z^{2} + 24 z + 140 = 0

98 x^{2} - 2 = 0

6 x^{2} + 2 = 34

What are the solutions to the equation 6x^2+3=-2x ?
The solutions to the equation 6x^2+3=-2x are x=-1/6+i(sqrt(17))/6 ,x=-1/6-i(sqrt(17))/6
Find the zeros of 6x^2+3=-2x
The zeros of 6x^2+3=-2x are x=-1/6+i(sqrt(17))/6 ,x=-1/6-i(sqrt(17))/6