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

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

Find the zeros of 2/3 x-1/2 x^2= 1/3

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

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

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

Solution steps

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

Find Least Common Multiplier of

3, 2 : 6

Multiply by LCM=

6

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

Simplify

4 x - 3 x^{2} = 2

Move

2

to the left side

4 x - 3 x^{2} - 2 = 0

Write in the standard form

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

- 3 x^{2} + 4 x - 2 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 ( - 3 ) ( - 2 )}{2 ( - 3 )}

Simplify

4^{2} - 4 (- 3) (- 2) : 22 i

x_{1, 2} = \frac{- 4 \pm 2 2 i}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- 4 + 2 2 i}{2 ( - 3 )}, x_{2} = \frac{- 4 - 2 2 i}{2 ( - 3 )}

x = \frac{- 4 + 2 2 i}{2 ( - 3 )} : \frac{2}{3} - i \frac{2}{3}

x = \frac{- 4 - 2 2 i}{2 ( - 3 )} : \frac{2}{3} + i \frac{2}{3}

The solutions to the quadratic equation are:

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

(x + 8)^{2} - 9 x = 52

4 x^{2} - 19 x - 30 = 0

2 x^{2} + x = 22 x + 11

2 x^{2} - 5 x = 33

x, 5 x^{2} + 5 y^{2} - 9 x - 14 y + 26 = 0

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