What are the solutions to the equation 5x-7x^2=7 ?

The solutions to the equation 5x-7x^2=7 are x= 5/14-i(3sqrt(19))/(14),x= 5/14+i(3sqrt(19))/(14)

Find the zeros of 5x-7x^2=7

The zeros of 5x-7x^2=7 are x= 5/14-i(3sqrt(19))/(14),x= 5/14+i(3sqrt(19))/(14)

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5 x - 7 x^{2} = 7

x = \frac{5}{14} - i \frac{3 19}{14}, x = \frac{5}{14} + i \frac{3 19}{14}

Solution steps

5 x - 7 x^{2} = 7

Move

7

to the left side

5 x - 7 x^{2} - 7 = 0

Write in the standard form

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

- 7 x^{2} + 5 x - 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 ( - 7 ) ( - 7 )}{2 ( - 7 )}

Simplify

5^{2} - 4 (- 7) (- 7) : 319 i

x_{1, 2} = \frac{- 5 \pm 3 19 i}{2 ( - 7 )}

Separate the solutions

x_{1} = \frac{- 5 + 3 19 i}{2 ( - 7 )}, x_{2} = \frac{- 5 - 3 19 i}{2 ( - 7 )}

x = \frac{- 5 + 3 19 i}{2 ( - 7 )} : \frac{5}{14} - i \frac{3 19}{14}

x = \frac{- 5 - 3 19 i}{2 ( - 7 )} : \frac{5}{14} + i \frac{3 19}{14}

The solutions to the quadratic equation are:

x = \frac{5}{14} - i \frac{3 19}{14}, x = \frac{5}{14} + i \frac{3 19}{14}

35 x^{2} - 2 = 7 - 14 x^{2}

4 x (3 x + 2) = 24 x + 16

x^{2} - 16 x + 3 x = 90

x (x + 4) = - 5

5 x^{2} + 3 x + 10 = 0

What are the solutions to the equation 5x-7x^2=7 ?
The solutions to the equation 5x-7x^2=7 are x= 5/14-i(3sqrt(19))/(14),x= 5/14+i(3sqrt(19))/(14)
Find the zeros of 5x-7x^2=7
The zeros of 5x-7x^2=7 are x= 5/14-i(3sqrt(19))/(14),x= 5/14+i(3sqrt(19))/(14)