What are the solutions to the equation 3-8v-5v^2=2v ?

The solutions to the equation 3-8v-5v^2=2v are v=-(5+2sqrt(10))/5 ,v=(2sqrt(10)-5)/5

Find the zeros of 3-8v-5v^2=2v

The zeros of 3-8v-5v^2=2v are v=-(5+2sqrt(10))/5 ,v=(2sqrt(10)-5)/5

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3 - 8 v - 5 v^{2} = 2 v

v = - \frac{5 + 2 10}{5}, v = \frac{2 10 - 5}{5}

Decimal Notation

v = - 2.26491 \dots, v = 0.26491 \dots

Solution steps

3 - 8 v - 5 v^{2} = 2 v

Move

2 v

to the left side

- 5 v^{2} - 10 v + 3 = 0

Solve with the quadratic formula

v_{1, 2} = \frac{- ( - 10 ) \pm ( - 10 ) ^{2} - 4 ( - 5 ) \cdot 3}{2 ( - 5 )}

(- 10)^{2} - 4 (- 5) \cdot 3 = 410

v_{1, 2} = \frac{- ( - 10 ) \pm 4 10}{2 ( - 5 )}

Separate the solutions

v_{1} = \frac{- ( - 10 ) + 4 10}{2 ( - 5 )}, v_{2} = \frac{- ( - 10 ) - 4 10}{2 ( - 5 )}

v = \frac{- ( - 10 ) + 4 10}{2 ( - 5 )} : - \frac{5 + 2 10}{5}

v = \frac{- ( - 10 ) - 4 10}{2 ( - 5 )} : \frac{2 10 - 5}{5}

The solutions to the quadratic equation are:

v = - \frac{5 + 2 10}{5}, v = \frac{2 10 - 5}{5}

x^{2} = \frac{81}{144}

- 4 x^{2} = 6 x

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

- 3 x^{2} + 17 x - 20 = 0

x, x^{2} + y^{2} + 1 = 0

What are the solutions to the equation 3-8v-5v^2=2v ?
The solutions to the equation 3-8v-5v^2=2v are v=-(5+2sqrt(10))/5 ,v=(2sqrt(10)-5)/5
Find the zeros of 3-8v-5v^2=2v
The zeros of 3-8v-5v^2=2v are v=-(5+2sqrt(10))/5 ,v=(2sqrt(10)-5)/5