What are the solutions to the equation v^2+v-19=4v ?

The solutions to the equation v^2+v-19=4v are v=(3+sqrt(85))/2 ,v=(3-sqrt(85))/2

Find the zeros of v^2+v-19=4v

The zeros of v^2+v-19=4v are v=(3+sqrt(85))/2 ,v=(3-sqrt(85))/2

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v^{2} + v - 19 = 4 v

v = \frac{3 + 85}{2}, v = \frac{3 - 85}{2}

Decimal Notation

v = 6.10977 \dots, v = - 3.10977 \dots

Solution steps

v^{2} + v - 19 = 4 v

Move

4 v

to the left side

v^{2} - 3 v - 19 = 0

Solve with the quadratic formula

v_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot ( - 19 )}{2 \cdot 1}

(- 3)^{2} - 4 \cdot 1 \cdot (- 19) = 85

v_{1, 2} = \frac{- ( - 3 ) \pm 85}{2 \cdot 1}

Separate the solutions

v_{1} = \frac{- ( - 3 ) + 85}{2 \cdot 1}, v_{2} = \frac{- ( - 3 ) - 85}{2 \cdot 1}

v = \frac{- ( - 3 ) + 85}{2 \cdot 1} : \frac{3 + 85}{2}

v = \frac{- ( - 3 ) - 85}{2 \cdot 1} : \frac{3 - 85}{2}

The solutions to the quadratic equation are:

v = \frac{3 + 85}{2}, v = \frac{3 - 85}{2}

- 2 x^{2} + 1 = 5 x

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

3 m^{2} + 20 m + 25 = 0

4 p^{2} + 6 p + 1 = 2 p

- 16 x^{2} + 14 x + 4 = 0

What are the solutions to the equation v^2+v-19=4v ?
The solutions to the equation v^2+v-19=4v are v=(3+sqrt(85))/2 ,v=(3-sqrt(85))/2
Find the zeros of v^2+v-19=4v
The zeros of v^2+v-19=4v are v=(3+sqrt(85))/2 ,v=(3-sqrt(85))/2