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

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

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

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

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

x = \frac{1}{2}, x = \frac{1}{3}

Decimal Notation

x = 0.5, x = 0.33333 \dots

Solution steps

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

Multiply both sides by

3

12 x^{2} - 6 (x - \frac{1}{3}) = 4 x

Expand

12 x^{2} - 6 (x - \frac{1}{3}) : 12 x^{2} - 6 x + 2

12 x^{2} - 6 x + 2 = 4 x

Move

4 x

to the left side

12 x^{2} - 10 x + 2 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 10 ) \pm ( - 10 ) ^{2} - 4 \cdot 12 \cdot 2}{2 \cdot 12}

(- 10)^{2} - 4 \cdot 12 \cdot 2 = 2

x_{1, 2} = \frac{- ( - 10 ) \pm 2}{2 \cdot 12}

Separate the solutions

x_{1} = \frac{- ( - 10 ) + 2}{2 \cdot 12}, x_{2} = \frac{- ( - 10 ) - 2}{2 \cdot 12}

x = \frac{- ( - 10 ) + 2}{2 \cdot 12} : \frac{1}{2}

x = \frac{- ( - 10 ) - 2}{2 \cdot 12} : \frac{1}{3}

The solutions to the quadratic equation are:

x = \frac{1}{2}, x = \frac{1}{3}

5 x^{2} + 17 x - 12 = 0

7 x^{2} - 16 = 0

2 x^{2} + 9 + 3 x = 5 x

x^{2} - 3 x + 20 = 0

x, x^{2} + y^{2} + z^{2} = 0

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