What are the solutions to the equation (x^2)/3-(x(x-1))/4-1=(x^2-1) ?

The solutions to the equation (x^2)/3-(x(x-1))/4-1=(x^2-1) are x=0,x= 3/11

Find the zeros of (x^2)/3-(x(x-1))/4-1=(x^2-1)

The zeros of (x^2)/3-(x(x-1))/4-1=(x^2-1) are x=0,x= 3/11

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\frac{x ^{2}}{3} - \frac{x ( x - 1 )}{4} - 1 = (x^{2} - 1)

x = 0, x = \frac{3}{11}

Decimal Notation

x = 0, x = 0.27272 \dots

Solution steps

\frac{x ^{2}}{3} - \frac{x ( x - 1 )}{4} - 1 = (x^{2} - 1)

Find Least Common Multiplier of

3, 4 : 12

Multiply by LCM=

12

\frac{x ^{2}}{3} \cdot 12 - \frac{x ( x - 1 )}{4} \cdot 12 - 1 \cdot 12 = (x^{2} - 1) \cdot 12

Simplify

4 x^{2} - 3 x (x - 1) - 12 = 12 (x^{2} - 1)

Expand

4 x^{2} - 3 x (x - 1) - 12 : x^{2} + 3 x - 12

Expand

12 (x^{2} - 1) : 12 x^{2} - 12

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

Move

12

to the left side

x^{2} + 3 x = 12 x^{2}

Move

12 x^{2}

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 ( - 11 ) \cdot 0}{2 ( - 11 )}

3^{2} - 4 (- 11) \cdot 0 = 3

x_{1, 2} = \frac{- 3 \pm 3}{2 ( - 11 )}

Separate the solutions

x_{1} = \frac{- 3 + 3}{2 ( - 11 )}, x_{2} = \frac{- 3 - 3}{2 ( - 11 )}

x = \frac{- 3 + 3}{2 ( - 11 )} : 0

x = \frac{- 3 - 3}{2 ( - 11 )} : \frac{3}{11}

The solutions to the quadratic equation are:

x = 0, x = \frac{3}{11}

3 x^{2} - 1 = 4 λ x, - y = 2 λ x, x^{2} + y^{2} = 1

2 a x^{2} + (3 a - 1) x + a + b = 0

x^{2} + 2 x + 7 = x + 7

- x^{2} + 2 x + 9 = 0

d^{2} = 50 - 23 d

What are the solutions to the equation (x^2)/3-(x(x-1))/4-1=(x^2-1) ?
The solutions to the equation (x^2)/3-(x(x-1))/4-1=(x^2-1) are x=0,x= 3/11
Find the zeros of (x^2)/3-(x(x-1))/4-1=(x^2-1)
The zeros of (x^2)/3-(x(x-1))/4-1=(x^2-1) are x=0,x= 3/11