What are the solutions to the equation x/6+(x^2)/2 =2 x/3 ?

The solutions to the equation x/6+(x^2)/2 =2 x/3 are x=1,x=0

Find the zeros of x/6+(x^2)/2 =2 x/3

The zeros of x/6+(x^2)/2 =2 x/3 are x=1,x=0

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\frac{x}{6} + \frac{x ^{2}}{2} = 2 \frac{x}{3}

x = 1, x = 0

Solution steps

\frac{x}{6} + \frac{x ^{2}}{2} = 2 \cdot \frac{x}{3}

Find Least Common Multiplier of

6, 2 : 6

Multiply by LCM=

6

\frac{x}{6} \cdot 6 + \frac{x ^{2}}{2} \cdot 6 = 2 \cdot \frac{x}{3} \cdot 6

Simplify

x + 3 x^{2} = 4 x

Move

4 x

to the left side

3 x^{2} - 3 x = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 3 \cdot 0}{2 \cdot 3}

(- 3)^{2} - 4 \cdot 3 \cdot 0 = 3

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

Separate the solutions

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

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

x = \frac{- ( - 3 ) - 3}{2 \cdot 3} : 0

The solutions to the quadratic equation are:

x = 1, x = 0

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

a, (a + b) 1 + a^{2} = c^{6}

k, p^{2} + q^{2} = k^{2}

(k - 12) \cdot x^{2} + 2 (k - 12) \cdot x + 2 = 0

2 \cdot x^{2} + 7 x + 52 = 0

What are the solutions to the equation x/6+(x^2)/2 =2 x/3 ?
The solutions to the equation x/6+(x^2)/2 =2 x/3 are x=1,x=0
Find the zeros of x/6+(x^2)/2 =2 x/3
The zeros of x/6+(x^2)/2 =2 x/3 are x=1,x=0