3k-18/(42-7k)

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Solution for 3k-18/(42-7k) equation:


D( k )

42-(7*k) = 0

42-(7*k) = 0

42-(7*k) = 0

42-7*k = 0

42-7*k = 0 // - 42

-7*k = -42 // : -7

k = -42/(-7)

k = 6

k in (-oo:6) U (6:+oo)

3*k-(18/(42-(7*k))) = 0

3*k-18*(42-7*k)^-1 = 0

3*k-18/(42-7*k) = 0

(3*k*(42-7*k))/(42-7*k)-18/(42-7*k) = 0

3*k*(42-7*k)-18 = 0

126*k-21*k^2-18 = 0

126*k-21*k^2-18 = 0

3*(42*k-7*k^2-6) = 0

42*k-7*k^2-6 = 0

DELTA = 42^2-(-7*(-6)*4)

DELTA = 1596

DELTA > 0

k = (1596^(1/2)-42)/(-7*2) or k = (-1596^(1/2)-42)/(-7*2)

k = (2*399^(1/2)-42)/(-14) or k = (-2*399^(1/2)-42)/(-14)

3*(k-((2*399^(1/2)-42)/(-14)))*(k-((-2*399^(1/2)-42)/(-14))) = 0

(3*(k-((2*399^(1/2)-42)/(-14)))*(k-((-2*399^(1/2)-42)/(-14))))/(42-7*k) = 0

(3*(k-((2*399^(1/2)-42)/(-14)))*(k-((-2*399^(1/2)-42)/(-14))))/(42-7*k) = 0 // * 42-7*k

3*(k-((2*399^(1/2)-42)/(-14)))*(k-((-2*399^(1/2)-42)/(-14))) = 0

( 3 )

3 = 0

k belongs to the empty set

( k-((-2*399^(1/2)-42)/(-14)) )

k-((-2*399^(1/2)-42)/(-14)) = 0 // + (-2*399^(1/2)-42)/(-14)

k = (-2*399^(1/2)-42)/(-14)

( k-((2*399^(1/2)-42)/(-14)) )

k-((2*399^(1/2)-42)/(-14)) = 0 // + (2*399^(1/2)-42)/(-14)

k = (2*399^(1/2)-42)/(-14)

k in { (-2*399^(1/2)-42)/(-14), (2*399^(1/2)-42)/(-14) }

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