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

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

Find the zeros of 2x(x-2)=x+3

The zeros of 2x(x-2)=x+3 are x=3,x=-1/2

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2 x (x - 2) = x + 3

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

Decimal Notation

x = 3, x = - 0.5

Solution steps

2 x (x - 2) = x + 3

Expand

2 x (x - 2) : 2 x^{2} - 4 x

2 x^{2} - 4 x = x + 3

Move

3

to the left side

2 x^{2} - 4 x - 3 = x

Move

x

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 2 ( - 3 )}{2 \cdot 2}

(- 5)^{2} - 4 \cdot 2 (- 3) = 7

x_{1, 2} = \frac{- ( - 5 ) \pm 7}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 5 ) + 7}{2 \cdot 2}, x_{2} = \frac{- ( - 5 ) - 7}{2 \cdot 2}

x = \frac{- ( - 5 ) + 7}{2 \cdot 2} : 3

x = \frac{- ( - 5 ) - 7}{2 \cdot 2} : - \frac{1}{2}

The solutions to the quadratic equation are:

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

x, - x^{2} + 2 x = y

x^{2} - 4 (2 + x) = 13

3 x^{2} - 10 x = 6 x - x^{2} - 15

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

- x^{2} + x + 6 = 0

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