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

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

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

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

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

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

Decimal Notation

x = 0, x = - 1.5

Solution steps

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

Expand

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

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

Move

5 x

to the left side

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

Move

x^{2}

to the left side

2 x^{2} + 3 x = 0

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

a^{2} - 3.4 a + 1.2 = 0

x^{2} - 7 x - 170 = 0

2 x^{2} - 7 x - 32 = 0

2 x^{2} + 5 x - 14 = 0

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

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