What are the solutions to the equation 3x(1-2x)=16 ?

The solutions to the equation 3x(1-2x)=16 are x= 1/4-i(5sqrt(15))/(12),x= 1/4+i(5sqrt(15))/(12)

Find the zeros of 3x(1-2x)=16

The zeros of 3x(1-2x)=16 are x= 1/4-i(5sqrt(15))/(12),x= 1/4+i(5sqrt(15))/(12)

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3 x (1 - 2 x) = 16

x = \frac{1}{4} - i \frac{5 15}{12}, x = \frac{1}{4} + i \frac{5 15}{12}

Solution steps

3 x (1 - 2 x) = 16

Expand

3 x (1 - 2 x) : 3 x - 6 x^{2}

3 x - 6 x^{2} = 16

Move

16

to the left side

3 x - 6 x^{2} - 16 = 0

Write in the standard form

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

- 6 x^{2} + 3 x - 16 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 ( - 6 ) ( - 16 )}{2 ( - 6 )}

Simplify

3^{2} - 4 (- 6) (- 16) : 515 i

x_{1, 2} = \frac{- 3 \pm 5 15 i}{2 ( - 6 )}

Separate the solutions

x_{1} = \frac{- 3 + 5 15 i}{2 ( - 6 )}, x_{2} = \frac{- 3 - 5 15 i}{2 ( - 6 )}

x = \frac{- 3 + 5 15 i}{2 ( - 6 )} : \frac{1}{4} - i \frac{5 15}{12}

x = \frac{- 3 - 5 15 i}{2 ( - 6 )} : \frac{1}{4} + i \frac{5 15}{12}

The solutions to the quadratic equation are:

x = \frac{1}{4} - i \frac{5 15}{12}, x = \frac{1}{4} + i \frac{5 15}{12}

5 x^{2} - 2 = - 9 x

x^{2} + 70 = 17 x

t (t) = 25 - 2 t

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

10 - 4 x - x^{2}

What are the solutions to the equation 3x(1-2x)=16 ?
The solutions to the equation 3x(1-2x)=16 are x= 1/4-i(5sqrt(15))/(12),x= 1/4+i(5sqrt(15))/(12)
Find the zeros of 3x(1-2x)=16
The zeros of 3x(1-2x)=16 are x= 1/4-i(5sqrt(15))/(12),x= 1/4+i(5sqrt(15))/(12)