What are the solutions to the equation 6x-2x^2=10 ?

The solutions to the equation 6x-2x^2=10 are x= 3/2-i(sqrt(11))/2 ,x= 3/2+i(sqrt(11))/2

Find the zeros of 6x-2x^2=10

The zeros of 6x-2x^2=10 are x= 3/2-i(sqrt(11))/2 ,x= 3/2+i(sqrt(11))/2

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6 x - 2 x^{2} = 10

x = \frac{3}{2} - i \frac{11}{2}, x = \frac{3}{2} + i \frac{11}{2}

Solution steps

6 x - 2 x^{2} = 10

Move

10

to the left side

6 x - 2 x^{2} - 10 = 0

Write in the standard form

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

- 2 x^{2} + 6 x - 10 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 ( - 2 ) ( - 10 )}{2 ( - 2 )}

Simplify

6^{2} - 4 (- 2) (- 10) : 211 i

x_{1, 2} = \frac{- 6 \pm 2 11 i}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- 6 + 2 11 i}{2 ( - 2 )}, x_{2} = \frac{- 6 - 2 11 i}{2 ( - 2 )}

x = \frac{- 6 + 2 11 i}{2 ( - 2 )} : \frac{3}{2} - i \frac{11}{2}

x = \frac{- 6 - 2 11 i}{2 ( - 2 )} : \frac{3}{2} + i \frac{11}{2}

The solutions to the quadratic equation are:

x = \frac{3}{2} - i \frac{11}{2}, x = \frac{3}{2} + i \frac{11}{2}

225 x^{2} - 16 = 33

x^{2} + 5 x = 14

x^{2} - x + 18 = - 8 x + 8

2 (x + 2)^{2} = 64

2 x^{2} - 8 x - 10 = 0

What are the solutions to the equation 6x-2x^2=10 ?
The solutions to the equation 6x-2x^2=10 are x= 3/2-i(sqrt(11))/2 ,x= 3/2+i(sqrt(11))/2
Find the zeros of 6x-2x^2=10
The zeros of 6x-2x^2=10 are x= 3/2-i(sqrt(11))/2 ,x= 3/2+i(sqrt(11))/2