What are the solutions to the equation 3x(x-3)=5x^2-10x ?

The solutions to the equation 3x(x-3)=5x^2-10x are x=0,x= 1/2

Find the zeros of 3x(x-3)=5x^2-10x

The zeros of 3x(x-3)=5x^2-10x are x=0,x= 1/2

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3 x (x - 3) = 5 x^{2} - 10 x

x = 0, x = \frac{1}{2}

Decimal Notation

x = 0, x = 0.5

Solution steps

3 x (x - 3) = 5 x^{2} - 10 x

Expand

3 x (x - 3) : 3 x^{2} - 9 x

3 x^{2} - 9 x = 5 x^{2} - 10 x

Move

10 x

to the left side

3 x^{2} + x = 5 x^{2}

Move

5 x^{2}

to the left side

- 2 x^{2} + x = 0

Solve with the quadratic formula

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

1^{2} - 4 (- 2) \cdot 0 = 1

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

Separate the solutions

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

x = \frac{- 1 + 1}{2 ( - 2 )} : 0

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

The solutions to the quadratic equation are:

x = 0, x = \frac{1}{2}

- x^{2} + 49

8^{\frac{7}{4}} \cdot 2^{\frac{7}{4}}

x^{2} - 5 x + 10 > 0

2 g^{2} + 7 g + 5

\frac{3}{10} + \frac{1}{20}

What are the solutions to the equation 3x(x-3)=5x^2-10x ?
The solutions to the equation 3x(x-3)=5x^2-10x are x=0,x= 1/2
Find the zeros of 3x(x-3)=5x^2-10x
The zeros of 3x(x-3)=5x^2-10x are x=0,x= 1/2