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

The solutions to the equation 2/3 x^2+x+3=0 are x=-3/4+i(3sqrt(7))/4 ,x=-3/4-i(3sqrt(7))/4

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

The zeros of 2/3 x^2+x+3=0 are x=-3/4+i(3sqrt(7))/4 ,x=-3/4-i(3sqrt(7))/4

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

x = - \frac{3}{4} + i \frac{3 7}{4}, x = - \frac{3}{4} - i \frac{3 7}{4}

Solution steps

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

Multiply both sides by

3

2 x^{2} + 3 x + 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 2 \cdot 9}{2 \cdot 2}

Simplify

3^{2} - 4 \cdot 2 \cdot 9 : 37 i

x_{1, 2} = \frac{- 3 \pm 3 7 i}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 3 + 3 7 i}{2 \cdot 2}, x_{2} = \frac{- 3 - 3 7 i}{2 \cdot 2}

x = \frac{- 3 + 3 7 i}{2 \cdot 2} : - \frac{3}{4} + i \frac{3 7}{4}

x = \frac{- 3 - 3 7 i}{2 \cdot 2} : - \frac{3}{4} - i \frac{3 7}{4}

The solutions to the quadratic equation are:

x = - \frac{3}{4} + i \frac{3 7}{4}, x = - \frac{3}{4} - i \frac{3 7}{4}

(x - 8) (x - 10) = - 1

- 15 - 17 x + 4 x^{2} = 0

- x^{2} - 4 x + 10

2 x^{2} + 11 x + 19 = 0

(x - 4)^{2} + (x + 2)^{2} = 25

What are the solutions to the equation 2/3 x^2+x+3=0 ?
The solutions to the equation 2/3 x^2+x+3=0 are x=-3/4+i(3sqrt(7))/4 ,x=-3/4-i(3sqrt(7))/4
Find the zeros of 2/3 x^2+x+3=0
The zeros of 2/3 x^2+x+3=0 are x=-3/4+i(3sqrt(7))/4 ,x=-3/4-i(3sqrt(7))/4