What are the solutions to the equation 0=0.5F(1-F/(3000))-10 ?

The solutions to the equation 0=0.5F(1-F/(3000))-10 are F=300(-sqrt(73/3)+5),F=300(sqrt(73/3)+5)

Find the zeros of 0=0.5F(1-F/(3000))-10

The zeros of 0=0.5F(1-F/(3000))-10 are F=300(-sqrt(73/3)+5),F=300(sqrt(73/3)+5)

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0 = 0.5 F (1 - \frac{F}{3000}) - 10

F = 300 (- \frac{73}{3} + 5), F = 300 (\frac{73}{3} + 5)

Decimal

F = 20.13514 \dots, F = 2979.86485 \dots

Solution steps

0 = 0.5 F (1 - \frac{F}{3000}) - 10

Multiply both sides by

10

0 = 5 F (1 - \frac{F}{3000}) - 100

Expand

5 F (1 - \frac{F}{3000}) - 100 : 5 F - \frac{F ^{2}}{600} - 100

0 = 5 F - \frac{F ^{2}}{600} - 100

Switch sides

5 F - \frac{F ^{2}}{600} - 100 = 0

Write in the standard form

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

- \frac{F ^{2}}{600} + 5 F - 100 = 0

Solve with the quadratic formula

F_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 ( - \frac{1}{600} ) ( - 100 )}{2 ( - \frac{1}{600} )}

5^{2} - 4 (- \frac{1}{600}) (- 100) = \frac{73}{3}

F_{1, 2} = \frac{- 5 \pm \frac{73}{3}}{2 ( - \frac{1}{600} )}

Separate the solutions

F_{1} = \frac{- 5 + \frac{73}{3}}{2 ( - \frac{1}{600} )}, F_{2} = \frac{- 5 - \frac{73}{3}}{2 ( - \frac{1}{600} )}

F = \frac{- 5 + \frac{73}{3}}{2 ( - \frac{1}{600} )} : 300 (- \frac{73}{3} + 5)

F = \frac{- 5 - \frac{73}{3}}{2 ( - \frac{1}{600} )} : 300 (\frac{73}{3} + 5)

The solutions to the quadratic equation are:

F = 300 (- \frac{73}{3} + 5), F = 300 (\frac{73}{3} + 5)

11 x^{2} - 12 x + 2 = 0

x, w = - 3 x^{2} + 5

4.1 x^{2} + 3 x - 50 = 0

0 = 4 x + x^{2}

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

What are the solutions to the equation 0=0.5F(1-F/(3000))-10 ?
The solutions to the equation 0=0.5F(1-F/(3000))-10 are F=300(-sqrt(73/3)+5),F=300(sqrt(73/3)+5)
Find the zeros of 0=0.5F(1-F/(3000))-10
The zeros of 0=0.5F(1-F/(3000))-10 are F=300(-sqrt(73/3)+5),F=300(sqrt(73/3)+5)