What are the solutions to the equation 3n^2-4n+9=3 ?

The solutions to the equation 3n^2-4n+9=3 are n= 2/3+i(sqrt(14))/3 ,n= 2/3-i(sqrt(14))/3

Find the zeros of 3n^2-4n+9=3

The zeros of 3n^2-4n+9=3 are n= 2/3+i(sqrt(14))/3 ,n= 2/3-i(sqrt(14))/3

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3 n^{2} - 4 n + 9 = 3

n = \frac{2}{3} + i \frac{14}{3}, n = \frac{2}{3} - i \frac{14}{3}

Solution steps

3 n^{2} - 4 n + 9 = 3

Move

3

to the left side

3 n^{2} - 4 n + 6 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 3 \cdot 6}{2 \cdot 3}

Simplify

(- 4)^{2} - 4 \cdot 3 \cdot 6 : 214 i

n_{1, 2} = \frac{- ( - 4 ) \pm 2 14 i}{2 \cdot 3}

Separate the solutions

n_{1} = \frac{- ( - 4 ) + 2 14 i}{2 \cdot 3}, n_{2} = \frac{- ( - 4 ) - 2 14 i}{2 \cdot 3}

n = \frac{- ( - 4 ) + 2 14 i}{2 \cdot 3} : \frac{2}{3} + i \frac{14}{3}

n = \frac{- ( - 4 ) - 2 14 i}{2 \cdot 3} : \frac{2}{3} - i \frac{14}{3}

The solutions to the quadratic equation are:

n = \frac{2}{3} + i \frac{14}{3}, n = \frac{2}{3} - i \frac{14}{3}

5 (x - 3)^{2} = 20

x^{2} + 8 + 12 = 0

(y - 1)^{2} - (y - 2)^{2} = y^{2}

x^{2} - 120 x + 7500 = 0

3 y^{2} + y - 1 = 0

What are the solutions to the equation 3n^2-4n+9=3 ?
The solutions to the equation 3n^2-4n+9=3 are n= 2/3+i(sqrt(14))/3 ,n= 2/3-i(sqrt(14))/3
Find the zeros of 3n^2-4n+9=3
The zeros of 3n^2-4n+9=3 are n= 2/3+i(sqrt(14))/3 ,n= 2/3-i(sqrt(14))/3