What are the solutions to the equation 2x-(x-1)^2=3x^2-6 ?

The solutions to the equation 2x-(x-1)^2=3x^2-6 are x=-(-1+sqrt(6))/2 ,x=(1+sqrt(6))/2

Find the zeros of 2x-(x-1)^2=3x^2-6

The zeros of 2x-(x-1)^2=3x^2-6 are x=-(-1+sqrt(6))/2 ,x=(1+sqrt(6))/2

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2 x - (x - 1)^{2} = 3 x^{2} - 6

x = - \frac{- 1 + 6}{2}, x = \frac{1 + 6}{2}

Decimal Notation

x = - 0.72474 \dots, x = 1.72474 \dots

Solution steps

2 x - (x - 1)^{2} = 3 x^{2} - 6

Expand

2 x - (x - 1)^{2} : - x^{2} + 4 x - 1

- x^{2} + 4 x - 1 = 3 x^{2} - 6

Move

6

to the left side

- x^{2} + 4 x + 5 = 3 x^{2}

Move

3 x^{2}

to the left side

- 4 x^{2} + 4 x + 5 = 0

Solve with the quadratic formula

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

4^{2} - 4 (- 4) \cdot 5 = 46

x_{1, 2} = \frac{- 4 \pm 4 6}{2 ( - 4 )}

Separate the solutions

x_{1} = \frac{- 4 + 4 6}{2 ( - 4 )}, x_{2} = \frac{- 4 - 4 6}{2 ( - 4 )}

x = \frac{- 4 + 4 6}{2 ( - 4 )} : - \frac{- 1 + 6}{2}

x = \frac{- 4 - 4 6}{2 ( - 4 )} : \frac{1 + 6}{2}

The solutions to the quadratic equation are:

x = - \frac{- 1 + 6}{2}, x = \frac{1 + 6}{2}

\frac{2 x - 3}{3 x - 5} > 3

3 x^{2} - 4 = 0

x^{8} - 256 x^{4}

3 = a (1 - 3)^{2} + (- 5)

(7)^{- 3}

What are the solutions to the equation 2x-(x-1)^2=3x^2-6 ?
The solutions to the equation 2x-(x-1)^2=3x^2-6 are x=-(-1+sqrt(6))/2 ,x=(1+sqrt(6))/2
Find the zeros of 2x-(x-1)^2=3x^2-6
The zeros of 2x-(x-1)^2=3x^2-6 are x=-(-1+sqrt(6))/2 ,x=(1+sqrt(6))/2