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

The solutions to the equation (x+1)3-(x-1)3=6x(x-3) are x=(3+sqrt(13))/2 ,x=(3-sqrt(13))/2

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

The zeros of (x+1)3-(x-1)3=6x(x-3) are x=(3+sqrt(13))/2 ,x=(3-sqrt(13))/2

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(x + 1) 3 - (x - 1) 3 = 6 x (x - 3)

x = \frac{3 + 13}{2}, x = \frac{3 - 13}{2}

Decimal Notation

x = 3.30277 \dots, x = - 0.30277 \dots

Solution steps

(x + 1) \cdot 3 - (x - 1) \cdot 3 = 6 x (x - 3)

Expand

(x + 1) \cdot 3 - (x - 1) \cdot 3 : 6

Expand

6 x (x - 3) : 6 x^{2} - 18 x

6 = 6 x^{2} - 18 x

Switch sides

6 x^{2} - 18 x = 6

Move

6

to the left side

6 x^{2} - 18 x - 6 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 18 ) \pm ( - 18 ) ^{2} - 4 \cdot 6 ( - 6 )}{2 \cdot 6}

(- 18)^{2} - 4 \cdot 6 (- 6) = 613

x_{1, 2} = \frac{- ( - 18 ) \pm 6 13}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- ( - 18 ) + 6 13}{2 \cdot 6}, x_{2} = \frac{- ( - 18 ) - 6 13}{2 \cdot 6}

x = \frac{- ( - 18 ) + 6 13}{2 \cdot 6} : \frac{3 + 13}{2}

x = \frac{- ( - 18 ) - 6 13}{2 \cdot 6} : \frac{3 - 13}{2}

The solutions to the quadratic equation are:

x = \frac{3 + 13}{2}, x = \frac{3 - 13}{2}

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

x^{2} - 7 x + 31 = 0

6 x^{2} - 726 = 0

k y^{2} + 2 (k + 4) y + 25 = 0

4 y^{2} + 8 y - 12 y - 7 = 0

What are the solutions to the equation (x+1)3-(x-1)3=6x(x-3) ?
The solutions to the equation (x+1)3-(x-1)3=6x(x-3) are x=(3+sqrt(13))/2 ,x=(3-sqrt(13))/2
Find the zeros of (x+1)3-(x-1)3=6x(x-3)
The zeros of (x+1)3-(x-1)3=6x(x-3) are x=(3+sqrt(13))/2 ,x=(3-sqrt(13))/2