What are the solutions to the equation -1/3 x^2+4/3 x-4/3 =-1/6 x^2+2/3 x-13/6 ?

The solutions to the equation -1/3 x^2+4/3 x-4/3 =-1/6 x^2+2/3 x-13/6 are x=-1,x=5

Find the zeros of -1/3 x^2+4/3 x-4/3 =-1/6 x^2+2/3 x-13/6

The zeros of -1/3 x^2+4/3 x-4/3 =-1/6 x^2+2/3 x-13/6 are x=-1,x=5

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- \frac{1}{3} x^{2} + \frac{4}{3} x - \frac{4}{3} = - \frac{1}{6} x^{2} + \frac{2}{3} x - \frac{13}{6}

x = - 1, x = 5

Solution steps

- \frac{1}{3} x^{2} + \frac{4}{3} x - \frac{4}{3} = - \frac{1}{6} x^{2} + \frac{2}{3} x - \frac{13}{6}

Find Least Common Multiplier of

3, 6 : 6

Multiply by LCM=

6

- \frac{1}{3} x^{2} \cdot 6 + \frac{4}{3} x \cdot 6 - \frac{4}{3} \cdot 6 = - \frac{1}{6} x^{2} \cdot 6 + \frac{2}{3} x \cdot 6 - \frac{13}{6} \cdot 6

Simplify

- 2 x^{2} + 8 x - 8 = - x^{2} + 4 x - 13

Move

13

to the left side

- 2 x^{2} + 8 x + 5 = - x^{2} + 4 x

Move

4 x

to the left side

- 2 x^{2} + 4 x + 5 = - x^{2}

Move

x^{2}

to the left side

- x^{2} + 4 x + 5 = 0

Solve with the quadratic formula

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

4^{2} - 4 (- 1) \cdot 5 = 6

x_{1, 2} = \frac{- 4 \pm 6}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 4 + 6}{2 ( - 1 )}, x_{2} = \frac{- 4 - 6}{2 ( - 1 )}

x = \frac{- 4 + 6}{2 ( - 1 )} : - 1

x = \frac{- 4 - 6}{2 ( - 1 )} : 5

The solutions to the quadratic equation are:

x = - 1, x = 5

15 x^{2} - 10 = 0

- 2 x^{2} + 6 x - 9 = 0

x, z = 6 - x^{2} - y^{2}

(k - 1) x^{2} + k^{2} x + 21 = 0

6 x^{2} = 10 + 11 x

What are the solutions to the equation -1/3 x^2+4/3 x-4/3 =-1/6 x^2+2/3 x-13/6 ?
The solutions to the equation -1/3 x^2+4/3 x-4/3 =-1/6 x^2+2/3 x-13/6 are x=-1,x=5
Find the zeros of -1/3 x^2+4/3 x-4/3 =-1/6 x^2+2/3 x-13/6
The zeros of -1/3 x^2+4/3 x-4/3 =-1/6 x^2+2/3 x-13/6 are x=-1,x=5