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

The solutions to the equation 5x-x^2=2x-3 are x=-(-3+sqrt(21))/2 ,x=(3+sqrt(21))/2

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

The zeros of 5x-x^2=2x-3 are x=-(-3+sqrt(21))/2 ,x=(3+sqrt(21))/2

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

x = - \frac{- 3 + 21}{2}, x = \frac{3 + 21}{2}

Decimal Notation

x = - 0.79128 \dots, x = 3.79128 \dots

Solution steps

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

Move

3

to the left side

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

Move

2 x

to the left side

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

Solve with the quadratic formula

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

3^{2} - 4 (- 1) \cdot 3 = 21

x_{1, 2} = \frac{- 3 \pm 21}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 3 + 21}{2 ( - 1 )}, x_{2} = \frac{- 3 - 21}{2 ( - 1 )}

x = \frac{- 3 + 21}{2 ( - 1 )} : - \frac{- 3 + 21}{2}

x = \frac{- 3 - 21}{2 ( - 1 )} : \frac{3 + 21}{2}

The solutions to the quadratic equation are:

x = - \frac{- 3 + 21}{2}, x = \frac{3 + 21}{2}

- 4 x^{2} - 40 x - 280 = 0

- 2 x^{2} + 2 x + 12 = 0

4 x^{2} + 256 = 0

- 3 x^{2} + 12 x + 429 = 0

4 (x - 2)^{2} = - 1

What are the solutions to the equation 5x-x^2=2x-3 ?
The solutions to the equation 5x-x^2=2x-3 are x=-(-3+sqrt(21))/2 ,x=(3+sqrt(21))/2
Find the zeros of 5x-x^2=2x-3
The zeros of 5x-x^2=2x-3 are x=-(-3+sqrt(21))/2 ,x=(3+sqrt(21))/2