What are the solutions to the equation solvefor m,f=(15m*30m)+20m^2 ?

The solutions to the equation solvefor m,f=(15m*30m)+20m^2 are m=sqrt(f/(470)),m=-sqrt(f/(470))

Find the zeros of solvefor m,f=(15m*30m)+20m^2

The zeros of solvefor m,f=(15m*30m)+20m^2 are m=sqrt(f/(470)),m=-sqrt(f/(470))

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solve for

m, f = (15 m \cdot 30 m) + 20 m^{2}

m = \frac{f}{470}, m = - \frac{f}{470}

Solution steps

f = (15 m \cdot 30 m) + 20 m^{2}

Expand

(15 m \cdot 30 m) + 20 m^{2} : 470 m^{2}

f = 470 m^{2}

Switch sides

470 m^{2} = f

Move

f

to the left side

470 m^{2} - f = 0

Solve with the quadratic formula

m_{1, 2} = \frac{- 0 \pm 0 ^{2} - 4 \cdot 470 ( - f )}{2 \cdot 470}

Simplify

0^{2} - 4 \cdot 470 (- f) : 2470 f

m_{1, 2} = \frac{- 0 \pm 2 470 f}{2 \cdot 470}

Separate the solutions

m_{1} = \frac{- 0 + 2 470 f}{2 \cdot 470}, m_{2} = \frac{- 0 - 2 470 f}{2 \cdot 470}

m = \frac{- 0 + 2 470 f}{2 \cdot 470} : \frac{f}{470}

m = \frac{- 0 - 2 470 f}{2 \cdot 470} : - \frac{f}{470}

The solutions to the quadratic equation are:

m = \frac{f}{470}, m = - \frac{f}{470}

8 x - 65 + x^{2} = 0

0 = - 3 x^{2} + 30 x + 600

b (b + 12) = 0

3 y^{2} + 8 y - 6 = 0

x^{2} + 3 x - 10

What are the solutions to the equation solvefor m,f=(15m*30m)+20m^2 ?
The solutions to the equation solvefor m,f=(15m*30m)+20m^2 are m=sqrt(f/(470)),m=-sqrt(f/(470))
Find the zeros of solvefor m,f=(15m*30m)+20m^2
The zeros of solvefor m,f=(15m*30m)+20m^2 are m=sqrt(f/(470)),m=-sqrt(f/(470))