What are the solutions to the equation 3v^2+10v+1=v ?

The solutions to the equation 3v^2+10v+1=v are v=(-9+sqrt(69))/6 ,v=(-9-sqrt(69))/6

Find the zeros of 3v^2+10v+1=v

The zeros of 3v^2+10v+1=v are v=(-9+sqrt(69))/6 ,v=(-9-sqrt(69))/6

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3 v^{2} + 10 v + 1 = v

v = \frac{- 9 + 69}{6}, v = \frac{- 9 - 69}{6}

Decimal Notation

v = - 0.11556 \dots, v = - 2.88443 \dots

Solution steps

3 v^{2} + 10 v + 1 = v

Move

v

to the left side

3 v^{2} + 9 v + 1 = 0

Solve with the quadratic formula

v_{1, 2} = \frac{- 9 \pm 9 ^{2} - 4 \cdot 3 \cdot 1}{2 \cdot 3}

9^{2} - 4 \cdot 3 \cdot 1 = 69

v_{1, 2} = \frac{- 9 \pm 69}{2 \cdot 3}

Separate the solutions

v_{1} = \frac{- 9 + 69}{2 \cdot 3}, v_{2} = \frac{- 9 - 69}{2 \cdot 3}

v = \frac{- 9 + 69}{2 \cdot 3} : \frac{- 9 + 69}{6}

v = \frac{- 9 - 69}{2 \cdot 3} : \frac{- 9 - 69}{6}

The solutions to the quadratic equation are:

v = \frac{- 9 + 69}{6}, v = \frac{- 9 - 69}{6}

y, x^{2} - x y + y^{2} = 0

y, 3 x^{2} + 2 x y + y^{2} = 2

x, c x^{2} + x + y^{2} = 0

4 x^{2} + 85 = - 36 x

- 2 x^{2} + 5 x - 6 = 0

What are the solutions to the equation 3v^2+10v+1=v ?
The solutions to the equation 3v^2+10v+1=v are v=(-9+sqrt(69))/6 ,v=(-9-sqrt(69))/6
Find the zeros of 3v^2+10v+1=v
The zeros of 3v^2+10v+1=v are v=(-9+sqrt(69))/6 ,v=(-9-sqrt(69))/6