What are the solutions to the equation x(3x-2)=-1 ?

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

Find the zeros of x(3x-2)=-1

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

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x (3 x - 2) = - 1

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

Solution steps

x (3 x - 2) = - 1

Expand

x (3 x - 2) : 3 x^{2} - 2 x

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

Move

1

to the left side

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}

3 m^{2} - 21 = 51

5 x^{2} + 19 x = - 12

2 x^{2} - 3 x - 15 = 4

j^{2} + 4 j + 4 = 0

4 x^{2} = - 8 x - 2

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