What are the solutions to the equation 5k^2+14k+1=4k ?

The solutions to the equation 5k^2+14k+1=4k are k=(-5+2sqrt(5))/5 ,k=-(sqrt(5)+2)/(sqrt(5))

Find the zeros of 5k^2+14k+1=4k

The zeros of 5k^2+14k+1=4k are k=(-5+2sqrt(5))/5 ,k=-(sqrt(5)+2)/(sqrt(5))

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5 k^{2} + 14 k + 1 = 4 k

k = \frac{- 5 + 2 5}{5}, k = - \frac{5 + 2}{5}

Decimal Notation

k = - 0.10557 \dots, k = - 1.89442 \dots

Solution steps

5 k^{2} + 14 k + 1 = 4 k

Move

4 k

to the left side

5 k^{2} + 10 k + 1 = 0

Solve with the quadratic formula

k_{1, 2} = \frac{- 10 \pm 1 0 ^{2} - 4 \cdot 5 \cdot 1}{2 \cdot 5}

1 0^{2} - 4 \cdot 5 \cdot 1 = 45

k_{1, 2} = \frac{- 10 \pm 4 5}{2 \cdot 5}

Separate the solutions

k_{1} = \frac{- 10 + 4 5}{2 \cdot 5}, k_{2} = \frac{- 10 - 4 5}{2 \cdot 5}

k = \frac{- 10 + 4 5}{2 \cdot 5} : \frac{- 5 + 2 5}{5}

k = \frac{- 10 - 4 5}{2 \cdot 5} : - \frac{5 + 2}{5}

The solutions to the quadratic equation are:

k = \frac{- 5 + 2 5}{5}, k = - \frac{5 + 2}{5}

2 m^{2} + m - 1 = 0

7 x^{2} - 8 x + 1 = 0

12 x^{2} - 72 x + 77 = 0

x^{2} = \frac{4}{25}

x^{2} + 6 x + 20 = 0

What are the solutions to the equation 5k^2+14k+1=4k ?
The solutions to the equation 5k^2+14k+1=4k are k=(-5+2sqrt(5))/5 ,k=-(sqrt(5)+2)/(sqrt(5))
Find the zeros of 5k^2+14k+1=4k
The zeros of 5k^2+14k+1=4k are k=(-5+2sqrt(5))/5 ,k=-(sqrt(5)+2)/(sqrt(5))