What are the solutions to the equation 8x^2+1=3x ?

The solutions to the equation 8x^2+1=3x are x= 3/16+i(sqrt(23))/(16),x= 3/16-i(sqrt(23))/(16)

Find the zeros of 8x^2+1=3x

The zeros of 8x^2+1=3x are x= 3/16+i(sqrt(23))/(16),x= 3/16-i(sqrt(23))/(16)

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8 x^{2} + 1 = 3 x

x = \frac{3}{16} + i \frac{23}{16}, x = \frac{3}{16} - i \frac{23}{16}

Solution steps

8 x^{2} + 1 = 3 x

Move

3 x

to the left side

8 x^{2} + 1 - 3 x = 0

Write in the standard form

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

8 x^{2} - 3 x + 1 = 0

Solve with the quadratic formula

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

Simplify

(- 3)^{2} - 4 \cdot 8 \cdot 1 : 23 i

x_{1, 2} = \frac{- ( - 3 ) \pm 23 i}{2 \cdot 8}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 23 i}{2 \cdot 8}, x_{2} = \frac{- ( - 3 ) - 23 i}{2 \cdot 8}

x = \frac{- ( - 3 ) + 23 i}{2 \cdot 8} : \frac{3}{16} + i \frac{23}{16}

x = \frac{- ( - 3 ) - 23 i}{2 \cdot 8} : \frac{3}{16} - i \frac{23}{16}

The solutions to the quadratic equation are:

x = \frac{3}{16} + i \frac{23}{16}, x = \frac{3}{16} - i \frac{23}{16}

- n^{2} + 5 n = 7 - 21

5 x^{2} - 2 x = 7

3 x^{2} + 5 x + 8 = 0

3 x^{2} + 12 x - 9 = 0

x^{2} + 18 x = 88

What are the solutions to the equation 8x^2+1=3x ?
The solutions to the equation 8x^2+1=3x are x= 3/16+i(sqrt(23))/(16),x= 3/16-i(sqrt(23))/(16)
Find the zeros of 8x^2+1=3x
The zeros of 8x^2+1=3x are x= 3/16+i(sqrt(23))/(16),x= 3/16-i(sqrt(23))/(16)