What are the solutions to the equation 11k^2=20+3k ?

The solutions to the equation 11k^2=20+3k are k=(3+sqrt(889))/(22),k=(3-sqrt(889))/(22)

Find the zeros of 11k^2=20+3k

The zeros of 11k^2=20+3k are k=(3+sqrt(889))/(22),k=(3-sqrt(889))/(22)

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11 k^{2} = 20 + 3 k

k = \frac{3 + 889}{22}, k = \frac{3 - 889}{22}

Decimal Notation

k = 1.49164 \dots, k = - 1.21891 \dots

Solution steps

11 k^{2} = 20 + 3 k

Move

3 k

to the left side

11 k^{2} - 3 k = 20

Move

20

to the left side

11 k^{2} - 3 k - 20 = 0

Solve with the quadratic formula

k_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 11 ( - 20 )}{2 \cdot 11}

(- 3)^{2} - 4 \cdot 11 (- 20) = 889

k_{1, 2} = \frac{- ( - 3 ) \pm 889}{2 \cdot 11}

Separate the solutions

k_{1} = \frac{- ( - 3 ) + 889}{2 \cdot 11}, k_{2} = \frac{- ( - 3 ) - 889}{2 \cdot 11}

k = \frac{- ( - 3 ) + 889}{2 \cdot 11} : \frac{3 + 889}{22}

k = \frac{- ( - 3 ) - 889}{2 \cdot 11} : \frac{3 - 889}{22}

The solutions to the quadratic equation are:

k = \frac{3 + 889}{22}, k = \frac{3 - 889}{22}

(2 x - 5)^{2} = - 2 (6 x - 11)

- x^{2} - 10 x + (- 9) = 0

3 - x^{2} = x

3 (x^{2} + 1) = - 3 x

(2 x - 1)^{2} - (x + 4)^{2} = 12 (5 - x)

What are the solutions to the equation 11k^2=20+3k ?
The solutions to the equation 11k^2=20+3k are k=(3+sqrt(889))/(22),k=(3-sqrt(889))/(22)
Find the zeros of 11k^2=20+3k
The zeros of 11k^2=20+3k are k=(3+sqrt(889))/(22),k=(3-sqrt(889))/(22)