What are the solutions to the equation 3x-2x^2=7 ?

The solutions to the equation 3x-2x^2=7 are x= 3/4-i(sqrt(47))/4 ,x= 3/4+i(sqrt(47))/4

Find the zeros of 3x-2x^2=7

The zeros of 3x-2x^2=7 are x= 3/4-i(sqrt(47))/4 ,x= 3/4+i(sqrt(47))/4

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3 x - 2 x^{2} = 7

x = \frac{3}{4} - i \frac{47}{4}, x = \frac{3}{4} + i \frac{47}{4}

Solution steps

3 x - 2 x^{2} = 7

Move

7

to the left side

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

Write in the standard form

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

- 2 x^{2} + 3 x - 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 ( - 2 ) ( - 7 )}{2 ( - 2 )}

Simplify

3^{2} - 4 (- 2) (- 7) : 47 i

x_{1, 2} = \frac{- 3 \pm 47 i}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- 3 + 47 i}{2 ( - 2 )}, x_{2} = \frac{- 3 - 47 i}{2 ( - 2 )}

x = \frac{- 3 + 47 i}{2 ( - 2 )} : \frac{3}{4} - i \frac{47}{4}

x = \frac{- 3 - 47 i}{2 ( - 2 )} : \frac{3}{4} + i \frac{47}{4}

The solutions to the quadratic equation are:

x = \frac{3}{4} - i \frac{47}{4}, x = \frac{3}{4} + i \frac{47}{4}

2 d^{2} + 11 d + 20 = d^{2}

6 x^{2} - 8 x = - 3

6 (x - 1)^{2} + 15 = 105

(3 x + 3)^{2} = 16

x^{2} = a

What are the solutions to the equation 3x-2x^2=7 ?
The solutions to the equation 3x-2x^2=7 are x= 3/4-i(sqrt(47))/4 ,x= 3/4+i(sqrt(47))/4
Find the zeros of 3x-2x^2=7
The zeros of 3x-2x^2=7 are x= 3/4-i(sqrt(47))/4 ,x= 3/4+i(sqrt(47))/4