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

The solutions to the equation 3/2 x^2+x/3+1=0 are x=-1/9+i(sqrt(53))/9 ,x=-1/9-i(sqrt(53))/9

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

The zeros of 3/2 x^2+x/3+1=0 are x=-1/9+i(sqrt(53))/9 ,x=-1/9-i(sqrt(53))/9

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

x = - \frac{1}{9} + i \frac{53}{9}, x = - \frac{1}{9} - i \frac{53}{9}

Solution steps

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

Find Least Common Multiplier of

2, 3 : 6

Multiply by LCM=

6

\frac{3}{2} x^{2} \cdot 6 + \frac{x}{3} \cdot 6 + 1 \cdot 6 = 0 \cdot 6

Simplify

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 9 \cdot 6}{2 \cdot 9}

Simplify

2^{2} - 4 \cdot 9 \cdot 6 : 253 i

x_{1, 2} = \frac{- 2 \pm 2 53 i}{2 \cdot 9}

Separate the solutions

x_{1} = \frac{- 2 + 2 53 i}{2 \cdot 9}, x_{2} = \frac{- 2 - 2 53 i}{2 \cdot 9}

x = \frac{- 2 + 2 53 i}{2 \cdot 9} : - \frac{1}{9} + i \frac{53}{9}

x = \frac{- 2 - 2 53 i}{2 \cdot 9} : - \frac{1}{9} - i \frac{53}{9}

The solutions to the quadratic equation are:

x = - \frac{1}{9} + i \frac{53}{9}, x = - \frac{1}{9} - i \frac{53}{9}

4 x^{2} + 16 x - 87 = - 3

0 = 12 x^{2} - 72 x + 81

x^{2} + 22 x + 120 = 0

x^{2} + 2 x - 5

x^{2} + 2 x - 8

What are the solutions to the equation 3/2 x^2+x/3+1=0 ?
The solutions to the equation 3/2 x^2+x/3+1=0 are x=-1/9+i(sqrt(53))/9 ,x=-1/9-i(sqrt(53))/9
Find the zeros of 3/2 x^2+x/3+1=0
The zeros of 3/2 x^2+x/3+1=0 are x=-1/9+i(sqrt(53))/9 ,x=-1/9-i(sqrt(53))/9