5k/7=40/k-15

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Solution for 5k/7=40/k-15 equation:


D( k )

k = 0

k = 0

k = 0

k in (-oo:0) U (0:+oo)

(5*k)/7 = 40/k-15 // - 40/k-15

(5*k)/7-(40/k)+15 = 0

(5*k)/7-40*k^-1+15 = 0

5/7*k^1-40*k^-1+15*k^0 = 0

(5/7*k^2+15*k^1-40*k^0)/(k^1) = 0 // * k^2

k^1*(5/7*k^2+15*k^1-40*k^0) = 0

k^1

(5/7)*k^2+15*k-40 = 0

(5/7)*k^2+15*k-40 = 0

DELTA = 15^2-(-40*4*(5/7))

DELTA = 2375/7

DELTA > 0

k = ((2375/7)^(1/2)-15)/(2*(5/7)) or k = (-(2375/7)^(1/2)-15)/(2*(5/7))

k = 7/10*((2375/7)^(1/2)-15) or k = -7/10*((2375/7)^(1/2)+15)

k in { -7/10*((2375/7)^(1/2)+15), 7/10*((2375/7)^(1/2)-15)}

k in { -7/10*((2375/7)^(1/2)+15), 7/10*((2375/7)^(1/2)-15) }

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