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

The solutions to the equation (x^2-4)/3-(6-x)/2 =3 are x=4,x=-11/2

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

The zeros of (x^2-4)/3-(6-x)/2 =3 are x=4,x=-11/2

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

x = 4, x = - \frac{11}{2}

Decimal

x = 4, x = - 5.5

Solution steps

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

Find Least Common Multiplier of

3, 2 : 6

Multiply by LCM=

6

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

Simplify

2 (x^{2} - 4) - 3 (- x + 6) = 18

Expand

2 (x^{2} - 4) - 3 (- x + 6) : 2 x^{2} + 3 x - 26

2 x^{2} + 3 x - 26 = 18

Move

18

to the left side

2 x^{2} + 3 x - 44 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 2 ( - 44 )}{2 \cdot 2}

3^{2} - 4 \cdot 2 (- 44) = 19

x_{1, 2} = \frac{- 3 \pm 19}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 3 + 19}{2 \cdot 2}, x_{2} = \frac{- 3 - 19}{2 \cdot 2}

x = \frac{- 3 + 19}{2 \cdot 2} : 4

x = \frac{- 3 - 19}{2 \cdot 2} : - \frac{11}{2}

The solutions to the quadratic equation are:

x = 4, x = - \frac{11}{2}

a^{2} + (- 2 a)^{2} = 4 0^{2}

2 x^{2} - 20 x + 41 = 0

a x^{2}

x^{2} + 4 x + 4

t, s = u t + \frac{1}{2} a t^{2}

What are the solutions to the equation (x^2-4)/3-(6-x)/2 =3 ?
The solutions to the equation (x^2-4)/3-(6-x)/2 =3 are x=4,x=-11/2
Find the zeros of (x^2-4)/3-(6-x)/2 =3
The zeros of (x^2-4)/3-(6-x)/2 =3 are x=4,x=-11/2