What are the solutions to the equation 3x^2+14x+53/2 =0 ?

The solutions to the equation 3x^2+14x+53/2 =0 are x=-7/3+i(sqrt(122))/6 ,x=-7/3-i(sqrt(122))/6

Find the zeros of 3x^2+14x+53/2 =0

The zeros of 3x^2+14x+53/2 =0 are x=-7/3+i(sqrt(122))/6 ,x=-7/3-i(sqrt(122))/6

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3 x^{2} + 14 x + \frac{53}{2} = 0

x = - \frac{7}{3} + i \frac{122}{6}, x = - \frac{7}{3} - i \frac{122}{6}

Solution steps

3 x^{2} + 14 x + \frac{53}{2} = 0

Multiply both sides by

2

6 x^{2} + 28 x + 53 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 28 \pm 2 8 ^{2} - 4 \cdot 6 \cdot 53}{2 \cdot 6}

Simplify

2 8^{2} - 4 \cdot 6 \cdot 53 : 2122 i

x_{1, 2} = \frac{- 28 \pm 2 122 i}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- 28 + 2 122 i}{2 \cdot 6}, x_{2} = \frac{- 28 - 2 122 i}{2 \cdot 6}

x = \frac{- 28 + 2 122 i}{2 \cdot 6} : - \frac{7}{3} + i \frac{122}{6}

x = \frac{- 28 - 2 122 i}{2 \cdot 6} : - \frac{7}{3} - i \frac{122}{6}

The solutions to the quadratic equation are:

x = - \frac{7}{3} + i \frac{122}{6}, x = - \frac{7}{3} - i \frac{122}{6}

9 x^{2} + 76 = 54 x

x, 2 x^{2} - 3 x y - 2 y^{2} = 0

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

10 x^{2} + 48 x + 72 = 0

2 x^{2} = 1 - 4 x

What are the solutions to the equation 3x^2+14x+53/2 =0 ?
The solutions to the equation 3x^2+14x+53/2 =0 are x=-7/3+i(sqrt(122))/6 ,x=-7/3-i(sqrt(122))/6
Find the zeros of 3x^2+14x+53/2 =0
The zeros of 3x^2+14x+53/2 =0 are x=-7/3+i(sqrt(122))/6 ,x=-7/3-i(sqrt(122))/6