What are the solutions to the equation (x^2-1)/6-(x-1)/4 =3 ?

The solutions to the equation (x^2-1)/6-(x-1)/4 =3 are x=5,x=-7/2

Find the zeros of (x^2-1)/6-(x-1)/4 =3

The zeros of (x^2-1)/6-(x-1)/4 =3 are x=5,x=-7/2

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\frac{x ^{2} - 1}{6} - \frac{x - 1}{4} = 3

x = 5, x = - \frac{7}{2}

Decimal Notation

x = 5, x = - 3.5

Solution steps

\frac{x ^{2} - 1}{6} - \frac{x - 1}{4} = 3

Find Least Common Multiplier of

6, 4 : 12

Multiply by LCM=

12

\frac{x ^{2} - 1}{6} \cdot 12 - \frac{x - 1}{4} \cdot 12 = 3 \cdot 12

Simplify

2 (x^{2} - 1) - 3 (x - 1) = 36

Expand

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

2 x^{2} - 3 x + 1 = 36

Move

36

to the left side

2 x^{2} - 3 x - 35 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 2 ( - 35 )}{2 \cdot 2}

(- 3)^{2} - 4 \cdot 2 (- 35) = 17

x_{1, 2} = \frac{- ( - 3 ) \pm 17}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 17}{2 \cdot 2}, x_{2} = \frac{- ( - 3 ) - 17}{2 \cdot 2}

x = \frac{- ( - 3 ) + 17}{2 \cdot 2} : 5

x = \frac{- ( - 3 ) - 17}{2 \cdot 2} : - \frac{7}{2}

The solutions to the quadratic equation are:

x = 5, x = - \frac{7}{2}

2 (x - 8)^{2} - 35 = 7

x^{2} - 5 x + 6 = 0

w, 30 w = 9 w^{2} + 25

d x^{2}

3 (x^{2} - 2) - 1 = 5

What are the solutions to the equation (x^2-1)/6-(x-1)/4 =3 ?
The solutions to the equation (x^2-1)/6-(x-1)/4 =3 are x=5,x=-7/2
Find the zeros of (x^2-1)/6-(x-1)/4 =3
The zeros of (x^2-1)/6-(x-1)/4 =3 are x=5,x=-7/2