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

The solutions to the equation 2x=3x^2 are x=0,x= 2/3

Find the zeros of 2x=3x^2

The zeros of 2x=3x^2 are x=0,x= 2/3

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2 x = 3 x^{2}

x = 0, x = \frac{2}{3}

Decimal Notation

x = 0, x = 0.66666 \dots

Solution steps

2 x = 3 x^{2}

Move

3 x^{2}

to the left side

2 x - 3 x^{2} = 0

Factor

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

- x (3 x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x - 2 = 0

Solve

3 x - 2 = 0 : x = \frac{2}{3}

The solutions to the quadratic equation are:

x = 0, x = \frac{2}{3}

2 x^{2} + 2 x = 4

\frac{x}{1000} = \frac{1}{2} (0.005) (6.5 - x - 0.5)^{2}

4 t^{2} + 2 t - 2 = 0

8 x^{2} - 2 x - 9 = 10

x^{2} = - 3 x + 18

What are the solutions to the equation 2x=3x^2 ?
The solutions to the equation 2x=3x^2 are x=0,x= 2/3
Find the zeros of 2x=3x^2
The zeros of 2x=3x^2 are x=0,x= 2/3