What are the solutions to the equation solvefor q,p=2+1/5 q+1/20 q^2 ?

The solutions to the equation solvefor q,p=2+1/5 q+1/20 q^2 are q=2(sqrt(5p-9)-1),q=-2(sqrt(5p-9)+1)

Find the zeros of solvefor q,p=2+1/5 q+1/20 q^2

The zeros of solvefor q,p=2+1/5 q+1/20 q^2 are q=2(sqrt(5p-9)-1),q=-2(sqrt(5p-9)+1)

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solve for

q, p = 2 + \frac{1}{5} q + \frac{1}{20} q^{2}

q = 2 (5 p - 9 - 1), q = - 2 (5 p - 9 + 1)

Solution steps

p = 2 + \frac{1}{5} q + \frac{1}{20} q^{2}

Find Least Common Multiplier of

5, 20 : 20

Multiply by LCM=

20

p \cdot 20 = 2 \cdot 20 + \frac{1}{5} q \cdot 20 + \frac{1}{20} q^{2} \cdot 20

Simplify

20 p = 40 + 4 q + q^{2}

Switch sides

40 + 4 q + q^{2} = 20 p

Move

20 p

to the left side

40 + 4 q + q^{2} - 20 p = 0

Write in the standard form

a x^{2} + b x + c = 0

q^{2} + 4 q + 40 - 20 p = 0

Solve with the quadratic formula

q_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot 1 \cdot ( 40 - 20 p )}{2 \cdot 1}

Simplify

4^{2} - 4 \cdot 1 \cdot (40 - 20 p) : 4 5 p - 9

q_{1, 2} = \frac{- 4 \pm 4 5 p - 9}{2 \cdot 1}

Separate the solutions

q_{1} = \frac{- 4 + 4 5 p - 9}{2 \cdot 1}, q_{2} = \frac{- 4 - 4 5 p - 9}{2 \cdot 1}

q = \frac{- 4 + 4 5 p - 9}{2 \cdot 1} : 2 (5 p - 9 - 1)

q = \frac{- 4 - 4 5 p - 9}{2 \cdot 1} : - 2 (5 p - 9 + 1)

The solutions to the quadratic equation are:

q = 2 (5 p - 9 - 1), q = - 2 (5 p - 9 + 1)

4 x^{2} - 3 x = 2

(10 - x) (- 12 - x) + 40 = 0

x (4 x - 1) = 3 x (x - 2) + 6

x, x^{2} - k x + 16 = 0

x^{2} = - 1 - 4 x

What are the solutions to the equation solvefor q,p=2+1/5 q+1/20 q^2 ?
The solutions to the equation solvefor q,p=2+1/5 q+1/20 q^2 are q=2(sqrt(5p-9)-1),q=-2(sqrt(5p-9)+1)
Find the zeros of solvefor q,p=2+1/5 q+1/20 q^2
The zeros of solvefor q,p=2+1/5 q+1/20 q^2 are q=2(sqrt(5p-9)-1),q=-2(sqrt(5p-9)+1)