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

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

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

The zeros of 1/4 n^2+3/2 n=-3/4 are n=-3+sqrt(6),n=-3-sqrt(6)

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

n = - 3 + 6, n = - 3 - 6

Decimal Notation

n = - 0.55051 \dots, n = - 5.44948 \dots

Solution steps

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

Find Least Common Multiplier of

4, 2 : 4

Multiply by LCM=

4

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

Simplify

n^{2} + 6 n = - 3

Move

3

to the left side

n^{2} + 6 n + 3 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 1 \cdot 3}{2 \cdot 1}

6^{2} - 4 \cdot 1 \cdot 3 = 26

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

n = - 3 + 6, n = - 3 - 6

- 2 x^{2} + 6 x - 4 = 0

x^{2} + 12 x y + 35 y^{2}

4 v^{3} - 12 v^{2} - 5 v + 15

- ln (3 + 32)

x^{2} + 7 x = 60

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