What are the solutions to the equation 3x^2-2x+4=3((x-1/3)+11/9) ?

The solutions to the equation 3x^2-2x+4=3((x-1/3)+11/9) are x= 4/3 ,x= 1/3

Find the zeros of 3x^2-2x+4=3((x-1/3)+11/9)

The zeros of 3x^2-2x+4=3((x-1/3)+11/9) are x= 4/3 ,x= 1/3

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3 x^{2} - 2 x + 4 = 3 ((x - \frac{1}{3}) + \frac{11}{9})

x = \frac{4}{3}, x = \frac{1}{3}

Solution steps

3 x^{2} - 2 x + 4 = 3 ((x - \frac{1}{3}) + \frac{11}{9})

Expand

3 ((x - \frac{1}{3}) + \frac{11}{9}) : 3 x + \frac{8}{3}

3 x^{2} - 2 x + 4 = 3 x + \frac{8}{3}

Move

\frac{8}{3}

to the left side

3 x^{2} - 2 x + \frac{4}{3} = 3 x

Move

3 x

to the left side

3 x^{2} - 5 x + \frac{4}{3} = 0

Solve with the quadratic formula

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

(- 5)^{2} - 4 \cdot 3 \cdot \frac{4}{3} = 3

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

Separate the solutions

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

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

x = \frac{- ( - 5 ) - 3}{2 \cdot 3} : \frac{1}{3}

The solutions to the quadratic equation are:

x = \frac{4}{3}, x = \frac{1}{3}

5 x 1 0^{- 2}

- 3 x + 5 > 17

x^{2} + 14 x + 13

5 x^{2} - 8 x = - 3

(\frac{9}{10})^{2}

What are the solutions to the equation 3x^2-2x+4=3((x-1/3)+11/9) ?
The solutions to the equation 3x^2-2x+4=3((x-1/3)+11/9) are x= 4/3 ,x= 1/3
Find the zeros of 3x^2-2x+4=3((x-1/3)+11/9)
The zeros of 3x^2-2x+4=3((x-1/3)+11/9) are x= 4/3 ,x= 1/3