What are the solutions to the equation 11n^2-4n=16 ?

The solutions to the equation 11n^2-4n=16 are n=(2(1+3sqrt(5)))/(11),n=(2(1-3sqrt(5)))/(11)

Find the zeros of 11n^2-4n=16

The zeros of 11n^2-4n=16 are n=(2(1+3sqrt(5)))/(11),n=(2(1-3sqrt(5)))/(11)

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11 n^{2} - 4 n = 16

n = \frac{2 ( 1 + 3 5 )}{11}, n = \frac{2 ( 1 - 3 5 )}{11}

Decimal Notation

n = 1.40149 \dots, n = - 1.03785 \dots

Solution steps

11 n^{2} - 4 n = 16

Move

16

to the left side

11 n^{2} - 4 n - 16 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 11 ( - 16 )}{2 \cdot 11}

(- 4)^{2} - 4 \cdot 11 (- 16) = 125

n_{1, 2} = \frac{- ( - 4 ) \pm 12 5}{2 \cdot 11}

Separate the solutions

n_{1} = \frac{- ( - 4 ) + 12 5}{2 \cdot 11}, n_{2} = \frac{- ( - 4 ) - 12 5}{2 \cdot 11}

n = \frac{- ( - 4 ) + 12 5}{2 \cdot 11} : \frac{2 ( 1 + 3 5 )}{11}

n = \frac{- ( - 4 ) - 12 5}{2 \cdot 11} : \frac{2 ( 1 - 3 5 )}{11}

The solutions to the quadratic equation are:

n = \frac{2 ( 1 + 3 5 )}{11}, n = \frac{2 ( 1 - 3 5 )}{11}

x^{2} - 2 + x = 0

x, x^{2} + 4 x + 2 = 0

(3 x - 8) (x - 3) = 0

9 x - 16 = 3 x - x^{2}

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

What are the solutions to the equation 11n^2-4n=16 ?
The solutions to the equation 11n^2-4n=16 are n=(2(1+3sqrt(5)))/(11),n=(2(1-3sqrt(5)))/(11)
Find the zeros of 11n^2-4n=16
The zeros of 11n^2-4n=16 are n=(2(1+3sqrt(5)))/(11),n=(2(1-3sqrt(5)))/(11)