What are the solutions to the equation 3x^3-x-10x=-x^2+2x ?

The solutions to the equation 3x^3-x-10x=-x^2+2x are x=0,x=(-1+sqrt(157))/6 ,x=(-1-sqrt(157))/6

Find the zeros of 3x^3-x-10x=-x^2+2x

The zeros of 3x^3-x-10x=-x^2+2x are x=0,x=(-1+sqrt(157))/6 ,x=(-1-sqrt(157))/6

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3 x^{3} - x - 10 x = - x^{2} + 2 x

x = 0, x = \frac{- 1 + 157}{6}, x = \frac{- 1 - 157}{6}

Decimal Notation

x = 0, x = 1.92166 \dots, x = - 2.25499 \dots

Solution steps

3 x^{3} - x - 10 x = - x^{2} + 2 x

Move

2 x

to the left side

3 x^{3} - 13 x = - x^{2}

Move

x^{2}

to the left side

3 x^{3} - 13 x + x^{2} = 0

Factor

3 x^{3} - 13 x + x^{2} : x (3 x^{2} + x - 13)

x (3 x^{2} + x - 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x^{2} + x - 13 = 0

Solve

3 x^{2} + x - 13 = 0 : x = \frac{- 1 + 157}{6}, x = \frac{- 1 - 157}{6}

The solutions are

x = 0, x = \frac{- 1 + 157}{6}, x = \frac{- 1 - 157}{6}

x^{4} - a^{4} = 0

x^{3} - 4 = 60

a (a^{2} - 2 a) = 0

x, x (x + 1) (x + 2) = - 1

x (x - 1) (x + 5) = 0

What are the solutions to the equation 3x^3-x-10x=-x^2+2x ?
The solutions to the equation 3x^3-x-10x=-x^2+2x are x=0,x=(-1+sqrt(157))/6 ,x=(-1-sqrt(157))/6
Find the zeros of 3x^3-x-10x=-x^2+2x
The zeros of 3x^3-x-10x=-x^2+2x are x=0,x=(-1+sqrt(157))/6 ,x=(-1-sqrt(157))/6