What are the solutions to the equation 1/2 x^2+1/6 x-1=0 ?

The solutions to the equation 1/2 x^2+1/6 x-1=0 are x=(-1+sqrt(73))/6 ,x=(-1-sqrt(73))/6

Find the zeros of 1/2 x^2+1/6 x-1=0

The zeros of 1/2 x^2+1/6 x-1=0 are x=(-1+sqrt(73))/6 ,x=(-1-sqrt(73))/6

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\frac{1}{2} x^{2} + \frac{1}{6} x - 1 = 0

x = \frac{- 1 + 73}{6}, x = \frac{- 1 - 73}{6}

Decimal Notation

x = 1.25733 \dots, x = - 1.59066 \dots

Solution steps

\frac{1}{2} x^{2} + \frac{1}{6} x - 1 = 0

Find Least Common Multiplier of

2, 6 : 6

Multiply by LCM=

6

\frac{1}{2} x^{2} \cdot 6 + \frac{1}{6} x \cdot 6 - 1 \cdot 6 = 0 \cdot 6

Simplify

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 3 ( - 6 )}{2 \cdot 3}

1^{2} - 4 \cdot 3 (- 6) = 73

x_{1, 2} = \frac{- 1 \pm 73}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- 1 + 73}{2 \cdot 3}, x_{2} = \frac{- 1 - 73}{2 \cdot 3}

x = \frac{- 1 + 73}{2 \cdot 3} : \frac{- 1 + 73}{6}

x = \frac{- 1 - 73}{2 \cdot 3} : \frac{- 1 - 73}{6}

The solutions to the quadratic equation are:

x = \frac{- 1 + 73}{6}, x = \frac{- 1 - 73}{6}

\frac{2}{5} + \frac{4}{3} \times \frac{3}{5} - (\frac{1}{4})^{2}

∣ x - 7 ∣ - 5 = 3

- 2 (x + 3) < 4

\frac{2 π}{500 π}

- 8 \cdot \frac{1}{4}

What are the solutions to the equation 1/2 x^2+1/6 x-1=0 ?
The solutions to the equation 1/2 x^2+1/6 x-1=0 are x=(-1+sqrt(73))/6 ,x=(-1-sqrt(73))/6
Find the zeros of 1/2 x^2+1/6 x-1=0
The zeros of 1/2 x^2+1/6 x-1=0 are x=(-1+sqrt(73))/6 ,x=(-1-sqrt(73))/6