What are the solutions to the equation solvefor x,3x^2-2x^3=0.5 ?

The solutions to the equation solvefor x,3x^2-2x^3=0.5 are x= 1/2 ,x=(1+sqrt(3))/2 ,x=(1-sqrt(3))/2

Find the zeros of solvefor x,3x^2-2x^3=0.5

The zeros of solvefor x,3x^2-2x^3=0.5 are x= 1/2 ,x=(1+sqrt(3))/2 ,x=(1-sqrt(3))/2

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solve for

x, 3 x^{2} - 2 x^{3} = 0.5

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

Decimal Notation

x = 0.5, x = 1.36602 \dots, x = - 0.36602 \dots

Solution steps

3 x^{2} - 2 x^{3} = 0.5

Multiply both sides by

10

30 x^{2} - 20 x^{3} = 5

Move

5

to the left side

30 x^{2} - 20 x^{3} - 5 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 20 x^{3} + 30 x^{2} - 5 = 0

Factor

- 20 x^{3} + 30 x^{2} - 5 : - 5 (2 x - 1) (2 x^{2} - 2 x - 1)

- 5 (2 x - 1) (2 x^{2} - 2 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x - 1 = 0 or 2 x^{2} - 2 x - 1 = 0

Solve

2 x - 1 = 0 : x = \frac{1}{2}

Solve

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

The solutions are

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

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

m^{3} - m^{2} = 0

2 x^{5} = 486

4 x^{3} + 12 x^{2} + 90 x + 40 = 0

y^{3} = - 3 y^{4}

What are the solutions to the equation solvefor x,3x^2-2x^3=0.5 ?
The solutions to the equation solvefor x,3x^2-2x^3=0.5 are x= 1/2 ,x=(1+sqrt(3))/2 ,x=(1-sqrt(3))/2
Find the zeros of solvefor x,3x^2-2x^3=0.5
The zeros of solvefor x,3x^2-2x^3=0.5 are x= 1/2 ,x=(1+sqrt(3))/2 ,x=(1-sqrt(3))/2