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

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

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

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

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

x = - \frac{1}{3}, x = - \frac{1}{2}

Decimal Notation

x = - 0.33333 \dots, x = - 0.5

Solution steps

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

Find Least Common Multiplier of

2, 6 : 6

Multiply by LCM=

6

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

Simplify

6 x (x + 1) - 3 = x - 4

Expand

6 x (x + 1) - 3 : 6 x^{2} + 6 x - 3

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

Move

4

to the left side

6 x^{2} + 6 x + 1 = x

Move

x

to the left side

6 x^{2} + 5 x + 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 \cdot 6 \cdot 1}{2 \cdot 6}

5^{2} - 4 \cdot 6 \cdot 1 = 1

x_{1, 2} = \frac{- 5 \pm 1}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- 5 + 1}{2 \cdot 6}, x_{2} = \frac{- 5 - 1}{2 \cdot 6}

x = \frac{- 5 + 1}{2 \cdot 6} : - \frac{1}{3}

x = \frac{- 5 - 1}{2 \cdot 6} : - \frac{1}{2}

The solutions to the quadratic equation are:

x = - \frac{1}{3}, x = - \frac{1}{2}

14 > - 2 x + 6 > - 6

- x + 23 = 2 - 2 (x - 8)

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

80 = - 22 + 6 x

9 + x^{2} = 25

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