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Math Help - Solve equation

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    29

    Solve equation

    Have I done this correctly

    6sinh(theta)-4cosh(theta)-3 =0
    My attempt-
    6(e^x-e^-x)/2- 4(e^x+e^-x)/2-3 =0
    3(e^x -e^-x) -2(e^x +e^-x) -3 =0
    e^x -e^-x-3 =0
    then -e^x = +/- 1 *square root(1^2 -4*1^2*(-3)/2

    Is this right
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  2. #2
    Member
    Joined
    Sep 2006
    Posts
    77
    6 \sinh(x)-4\cosh(x)-3=0
    3(e^x-e^{-x})-2(e^x+e^{-x})-3=0
    Now multiply everything by e^x (\neq 0)
    3e^{2x}-3-2e^{2x}-2-3e^x=0
    e^{2x}-3e^x-5=0
    e^x=\frac{3\pm\sqrt{9+20}}{2}
    e^x=\frac{3+\sqrt{29}}{2}~or~\frac{3-\sqrt{29}}{2}
    x=\ln(\frac{3+\sqrt{29}}{2})~or~\ln(\frac{3-\sqrt{29}}{2})
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