What are the solutions to the equation 8x^2+3=-4x ?

The solutions to the equation 8x^2+3=-4x are x=-1/4+i(sqrt(5))/4 ,x=-1/4-i(sqrt(5))/4

Find the zeros of 8x^2+3=-4x

The zeros of 8x^2+3=-4x are x=-1/4+i(sqrt(5))/4 ,x=-1/4-i(sqrt(5))/4

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8 x^{2} + 3 = - 4 x

x = - \frac{1}{4} + i \frac{5}{4}, x = - \frac{1}{4} - i \frac{5}{4}

Solution steps

8 x^{2} + 3 = - 4 x

Move

4 x

to the left side

8 x^{2} + 3 + 4 x = 0

Write in the standard form

a x^{2} + b x + c = 0

8 x^{2} + 4 x + 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot 8 \cdot 3}{2 \cdot 8}

Simplify

4^{2} - 4 \cdot 8 \cdot 3 : 45 i

x_{1, 2} = \frac{- 4 \pm 4 5 i}{2 \cdot 8}

Separate the solutions

x_{1} = \frac{- 4 + 4 5 i}{2 \cdot 8}, x_{2} = \frac{- 4 - 4 5 i}{2 \cdot 8}

x = \frac{- 4 + 4 5 i}{2 \cdot 8} : - \frac{1}{4} + i \frac{5}{4}

x = \frac{- 4 - 4 5 i}{2 \cdot 8} : - \frac{1}{4} - i \frac{5}{4}

The solutions to the quadratic equation are:

x = - \frac{1}{4} + i \frac{5}{4}, x = - \frac{1}{4} - i \frac{5}{4}

3 n^{2} + n - 310 = 0

x^{2} - 20 x - 12 = - 3

4 x^{2} + 32 x

4 x^{2} = 9 x + 28

x^{2} + 3 x + 8 = 0

What are the solutions to the equation 8x^2+3=-4x ?
The solutions to the equation 8x^2+3=-4x are x=-1/4+i(sqrt(5))/4 ,x=-1/4-i(sqrt(5))/4
Find the zeros of 8x^2+3=-4x
The zeros of 8x^2+3=-4x are x=-1/4+i(sqrt(5))/4 ,x=-1/4-i(sqrt(5))/4