What are the solutions to the equation 4k(k+3)=-15 ?

The solutions to the equation 4k(k+3)=-15 are k=-3/2+isqrt(3/2),k=-3/2-isqrt(3/2)

Find the zeros of 4k(k+3)=-15

The zeros of 4k(k+3)=-15 are k=-3/2+isqrt(3/2),k=-3/2-isqrt(3/2)

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4 k (k + 3) = - 15

k = - \frac{3}{2} + i \frac{3}{2}, k = - \frac{3}{2} - i \frac{3}{2}

Solution steps

4 k (k + 3) = - 15

Expand

4 k (k + 3) : 4 k^{2} + 12 k

4 k^{2} + 12 k = - 15

Move

15

to the left side

4 k^{2} + 12 k + 15 = 0

Solve with the quadratic formula

k_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 4 \cdot 15}{2 \cdot 4}

Simplify

1 2^{2} - 4 \cdot 4 \cdot 15 : 46 i

k_{1, 2} = \frac{- 12 \pm 4 6 i}{2 \cdot 4}

Separate the solutions

k_{1} = \frac{- 12 + 4 6 i}{2 \cdot 4}, k_{2} = \frac{- 12 - 4 6 i}{2 \cdot 4}

k = \frac{- 12 + 4 6 i}{2 \cdot 4} : - \frac{3}{2} + i \frac{3}{2}

k = \frac{- 12 - 4 6 i}{2 \cdot 4} : - \frac{3}{2} - i \frac{3}{2}

The solutions to the quadratic equation are:

k = - \frac{3}{2} + i \frac{3}{2}, k = - \frac{3}{2} - i \frac{3}{2}

s^{2} + 5 s + 9 = 0

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

3 x^{2} + 11 x = 42

3 x^{2} - 3 x = 1

- 2 x^{2} - x + 12 = - 3 x^{2} + 6 x

What are the solutions to the equation 4k(k+3)=-15 ?
The solutions to the equation 4k(k+3)=-15 are k=-3/2+isqrt(3/2),k=-3/2-isqrt(3/2)
Find the zeros of 4k(k+3)=-15
The zeros of 4k(k+3)=-15 are k=-3/2+isqrt(3/2),k=-3/2-isqrt(3/2)