What are the solutions to the equation 6x-5x^2=8 ?

The solutions to the equation 6x-5x^2=8 are x= 3/5-i(sqrt(31))/5 ,x= 3/5+i(sqrt(31))/5

Find the zeros of 6x-5x^2=8

The zeros of 6x-5x^2=8 are x= 3/5-i(sqrt(31))/5 ,x= 3/5+i(sqrt(31))/5

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6 x - 5 x^{2} = 8

x = \frac{3}{5} - i \frac{31}{5}, x = \frac{3}{5} + i \frac{31}{5}

Solution steps

6 x - 5 x^{2} = 8

Move

8

to the left side

6 x - 5 x^{2} - 8 = 0

Write in the standard form

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

- 5 x^{2} + 6 x - 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 ( - 5 ) ( - 8 )}{2 ( - 5 )}

Simplify

6^{2} - 4 (- 5) (- 8) : 231 i

x_{1, 2} = \frac{- 6 \pm 2 31 i}{2 ( - 5 )}

Separate the solutions

x_{1} = \frac{- 6 + 2 31 i}{2 ( - 5 )}, x_{2} = \frac{- 6 - 2 31 i}{2 ( - 5 )}

x = \frac{- 6 + 2 31 i}{2 ( - 5 )} : \frac{3}{5} - i \frac{31}{5}

x = \frac{- 6 - 2 31 i}{2 ( - 5 )} : \frac{3}{5} + i \frac{31}{5}

The solutions to the quadratic equation are:

x = \frac{3}{5} - i \frac{31}{5}, x = \frac{3}{5} + i \frac{31}{5}

m^{2} = m + 2

2 x (x + 5) = 3 (x - 1)

2 x^{2} - 9 x + 3 = - 4 x

x^{2} + x - \frac{1}{3} = 0

x^{2} - 4 = 2 x - 1

What are the solutions to the equation 6x-5x^2=8 ?
The solutions to the equation 6x-5x^2=8 are x= 3/5-i(sqrt(31))/5 ,x= 3/5+i(sqrt(31))/5
Find the zeros of 6x-5x^2=8
The zeros of 6x-5x^2=8 are x= 3/5-i(sqrt(31))/5 ,x= 3/5+i(sqrt(31))/5