What are the solutions to the equation 2x-3x^2=5 ?

The solutions to the equation 2x-3x^2=5 are x= 1/3-i(sqrt(14))/3 ,x= 1/3+i(sqrt(14))/3

Find the zeros of 2x-3x^2=5

The zeros of 2x-3x^2=5 are x= 1/3-i(sqrt(14))/3 ,x= 1/3+i(sqrt(14))/3

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2 x - 3 x^{2} = 5

x = \frac{1}{3} - i \frac{14}{3}, x = \frac{1}{3} + i \frac{14}{3}

Solution steps

2 x - 3 x^{2} = 5

Move

5

to the left side

2 x - 3 x^{2} - 5 = 0

Write in the standard form

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

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 ( - 3 ) ( - 5 )}{2 ( - 3 )}

Simplify

2^{2} - 4 (- 3) (- 5) : 214 i

x_{1, 2} = \frac{- 2 \pm 2 14 i}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- 2 + 2 14 i}{2 ( - 3 )}, x_{2} = \frac{- 2 - 2 14 i}{2 ( - 3 )}

x = \frac{- 2 + 2 14 i}{2 ( - 3 )} : \frac{1}{3} - i \frac{14}{3}

x = \frac{- 2 - 2 14 i}{2 ( - 3 )} : \frac{1}{3} + i \frac{14}{3}

The solutions to the quadratic equation are:

x = \frac{1}{3} - i \frac{14}{3}, x = \frac{1}{3} + i \frac{14}{3}

(3 x + 2)^{2} = 4

x^{2} - 9 x + 15 = 0

135 = (2 y + 3) (2 y - 3)

3 x^{2} - x = 5

x^{2} - 6 = 2 - 18 x

What are the solutions to the equation 2x-3x^2=5 ?
The solutions to the equation 2x-3x^2=5 are x= 1/3-i(sqrt(14))/3 ,x= 1/3+i(sqrt(14))/3
Find the zeros of 2x-3x^2=5
The zeros of 2x-3x^2=5 are x= 1/3-i(sqrt(14))/3 ,x= 1/3+i(sqrt(14))/3