What are the solutions to the equation 1/2 x^2+1/4 x-1/6 =0 ?

The solutions to the equation 1/2 x^2+1/4 x-1/6 =0 are x=(-3+sqrt(57))/(12),x=(-3-sqrt(57))/(12)

Find the zeros of 1/2 x^2+1/4 x-1/6 =0

The zeros of 1/2 x^2+1/4 x-1/6 =0 are x=(-3+sqrt(57))/(12),x=(-3-sqrt(57))/(12)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{1}{2} x^{2} + \frac{1}{4} x - \frac{1}{6} = 0

x = \frac{- 3 + 57}{12}, x = \frac{- 3 - 57}{12}

Decimal Notation

x = 0.37915 \dots, x = - 0.87915 \dots

Solution steps

\frac{1}{2} x^{2} + \frac{1}{4} x - \frac{1}{6} = 0

Find Least Common Multiplier of

2, 4, 6 : 12

Multiply by LCM=

12

\frac{1}{2} x^{2} \cdot 12 + \frac{1}{4} x \cdot 12 - \frac{1}{6} \cdot 12 = 0 \cdot 12

Simplify

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

Solve with the quadratic formula

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

3^{2} - 4 \cdot 6 (- 2) = 57

x_{1, 2} = \frac{- 3 \pm 57}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- 3 + 57}{2 \cdot 6}, x_{2} = \frac{- 3 - 57}{2 \cdot 6}

x = \frac{- 3 + 57}{2 \cdot 6} : \frac{- 3 + 57}{12}

x = \frac{- 3 - 57}{2 \cdot 6} : \frac{- 3 - 57}{12}

The solutions to the quadratic equation are:

x = \frac{- 3 + 57}{12}, x = \frac{- 3 - 57}{12}

n^{2} - 16 = 0

x^{2} + 10 x + 25

x^{2} - 2 x + 1 = 0

x^{2} + 1.2 x + 0.56 = 0

x^{2} + 2 x + \frac{5}{4} = 0

What are the solutions to the equation 1/2 x^2+1/4 x-1/6 =0 ?
The solutions to the equation 1/2 x^2+1/4 x-1/6 =0 are x=(-3+sqrt(57))/(12),x=(-3-sqrt(57))/(12)
Find the zeros of 1/2 x^2+1/4 x-1/6 =0
The zeros of 1/2 x^2+1/4 x-1/6 =0 are x=(-3+sqrt(57))/(12),x=(-3-sqrt(57))/(12)