What are the solutions to the equation 3x^2+3x+1/2 =0 ?

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

Find the zeros of 3x^2+3x+1/2 =0

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

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3 x^{2} + 3 x + \frac{1}{2} = 0

x = \frac{- 3 + 3}{6}, x = - \frac{3 + 1}{2 3}

Decimal

x = - 0.21132 \dots, x = - 0.78867 \dots

Solution steps

3 x^{2} + 3 x + \frac{1}{2} = 0

Multiply both sides by

2

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

Solve with the quadratic formula

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

6^{2} - 4 \cdot 6 \cdot 1 = 23

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = \frac{- 3 + 3}{6}, x = - \frac{3 + 1}{2 3}

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

x^{2} - x - 8 = 2 x^{2} - 2 x - 14

x, 4 x^{2} + 11 x = - 6

x^{2} - 0.5 x + 0.5 = 0

0 = - x^{2} + 12 x

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