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

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

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

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

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

x = 3, x = 5

Solution steps

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

Expand

3 x (x - 2) - x^{2} : 2 x^{2} - 6 x

Expand

(x - 3) (x + 5) : x^{2} + 2 x - 15

2 x^{2} - 6 x = x^{2} + 2 x - 15

Switch sides

x^{2} + 2 x - 15 = 2 x^{2} - 6 x

Move

6 x

to the left side

x^{2} + 8 x - 15 = 2 x^{2}

Move

2 x^{2}

to the left side

- x^{2} + 8 x - 15 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 ( - 1 ) ( - 15 )}{2 ( - 1 )}

8^{2} - 4 (- 1) (- 15) = 2

x_{1, 2} = \frac{- 8 \pm 2}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 8 + 2}{2 ( - 1 )}, x_{2} = \frac{- 8 - 2}{2 ( - 1 )}

x = \frac{- 8 + 2}{2 ( - 1 )} : 3

x = \frac{- 8 - 2}{2 ( - 1 )} : 5

The solutions to the quadratic equation are:

x = 3, x = 5

x^{2} + 5 x + 5

x^{2} + 5 x + 9

6 m^{2} + 3 m + 2 = 0

20 = - 2.7 t^{2} + 40 t + 6.5

2 (x + 2) (x - 2) = 0

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