What are the solutions to the equation 1/2 n^2+3/4 n=-1/12 ?

The solutions to the equation 1/2 n^2+3/4 n=-1/12 are n=(-9+sqrt(57))/(12),n=(-9-sqrt(57))/(12)

Find the zeros of 1/2 n^2+3/4 n=-1/12

The zeros of 1/2 n^2+3/4 n=-1/12 are n=(-9+sqrt(57))/(12),n=(-9-sqrt(57))/(12)

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\frac{1}{2} n^{2} + \frac{3}{4} n = - \frac{1}{12}

n = \frac{- 9 + 57}{12}, n = \frac{- 9 - 57}{12}

Decimal Notation

n = - 0.12084 \dots, n = - 1.37915 \dots

Solution steps

\frac{1}{2} n^{2} + \frac{3}{4} n = - \frac{1}{12}

Find Least Common Multiplier of

2, 4, 12 : 12

Multiply by LCM=

12

\frac{1}{2} n^{2} \cdot 12 + \frac{3}{4} n \cdot 12 = - \frac{1}{12} \cdot 12

Simplify

6 n^{2} + 9 n = - 1

Move

1

to the left side

6 n^{2} + 9 n + 1 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- 9 \pm 9 ^{2} - 4 \cdot 6 \cdot 1}{2 \cdot 6}

9^{2} - 4 \cdot 6 \cdot 1 = 57

n_{1, 2} = \frac{- 9 \pm 57}{2 \cdot 6}

Separate the solutions

n_{1} = \frac{- 9 + 57}{2 \cdot 6}, n_{2} = \frac{- 9 - 57}{2 \cdot 6}

n = \frac{- 9 + 57}{2 \cdot 6} : \frac{- 9 + 57}{12}

n = \frac{- 9 - 57}{2 \cdot 6} : \frac{- 9 - 57}{12}

The solutions to the quadratic equation are:

n = \frac{- 9 + 57}{12}, n = \frac{- 9 - 57}{12}

50 x^{3} + 160 x^{2} y + 128 x y^{2}

96 n^{3} - 84 n^{2} + 112 n - 98

- 2 (3 x + 6) \geq 4 (x + 7)

(- 2 i)^{3}

2 7^{2} + x^{2} = 4 5^{2}

What are the solutions to the equation 1/2 n^2+3/4 n=-1/12 ?
The solutions to the equation 1/2 n^2+3/4 n=-1/12 are n=(-9+sqrt(57))/(12),n=(-9-sqrt(57))/(12)
Find the zeros of 1/2 n^2+3/4 n=-1/12
The zeros of 1/2 n^2+3/4 n=-1/12 are n=(-9+sqrt(57))/(12),n=(-9-sqrt(57))/(12)