What are the solutions to the equation 3x^2-4x=-3 ?

The solutions to the equation 3x^2-4x=-3 are x= 2/3+i(sqrt(5))/3 ,x= 2/3-i(sqrt(5))/3

Find the zeros of 3x^2-4x=-3

The zeros of 3x^2-4x=-3 are x= 2/3+i(sqrt(5))/3 ,x= 2/3-i(sqrt(5))/3

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

x = \frac{2}{3} + i \frac{5}{3}, x = \frac{2}{3} - i \frac{5}{3}

Solution steps

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

Move

3

to the left side

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

Solve with the quadratic formula

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

Simplify

(- 4)^{2} - 4 \cdot 3 \cdot 3 : 25 i

x_{1, 2} = \frac{- ( - 4 ) \pm 2 5 i}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 5 i}{2 \cdot 3}, x_{2} = \frac{- ( - 4 ) - 2 5 i}{2 \cdot 3}

x = \frac{- ( - 4 ) + 2 5 i}{2 \cdot 3} : \frac{2}{3} + i \frac{5}{3}

x = \frac{- ( - 4 ) - 2 5 i}{2 \cdot 3} : \frac{2}{3} - i \frac{5}{3}

The solutions to the quadratic equation are:

x = \frac{2}{3} + i \frac{5}{3}, x = \frac{2}{3} - i \frac{5}{3}

5 x (x - 2) - 3 x = \frac{8}{3}

(x + 3)^{2} = - x - 1

x^{2} - 2 x = - 7

3 x^{2} + 2 x - 8 = x^{2} + 2 (x - 2)

x^{2} - \frac{1}{25} = 0

What are the solutions to the equation 3x^2-4x=-3 ?
The solutions to the equation 3x^2-4x=-3 are x= 2/3+i(sqrt(5))/3 ,x= 2/3-i(sqrt(5))/3
Find the zeros of 3x^2-4x=-3
The zeros of 3x^2-4x=-3 are x= 2/3+i(sqrt(5))/3 ,x= 2/3-i(sqrt(5))/3