Question 495518
{{{ 3x^(-2) - 7x^(-1) - 6 = 0 }}}
{{{ 3x^(-2) - 7x^(-1) = 6 }}}
{{{ 3/x^2  -  7/x = 6 }}}
Multiply both sides by {{{ x^2 }}}
{{{ 3 - 7x = 6x^2 }}}
{{{ 6x^2 + 7x - 3 = 0 }}}
Use the quadratic formula
{{{ x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = 6 }}}
{{{ b = 7 }}}
{{{ c = -3 }}}
{{{ x = (-7 +- sqrt( 7^2-4*6*(-3) ))/(2*6) }}} 
{{{ x = (-7 +- sqrt( 49 + 72 )) / 12 }}} 
{{{ x = (-7 +- sqrt( 121 )) / 12 }}} 
{{{ x = ( -7 + 11 ) / 12 }}}
{{{ x = 1/3 }}} 
and
{{{ x = (-7 - 11 ) / 12 }}}
{{{ x = -3/2 }}}
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check answers:
{{{ 3x^(-2) - 7x^(-1) - 6 = 0 }}}
{{{ 3*(1/3)^(-2) - 7*(1/3)^(-1) - 6 = 0 }}}
{{{ 3*9 - 7*3 - 6 = 0 }}}
{{{ 27 - 21 - 6 = 0 }}}
{{{ 6 - 6 = 0 }}}
OK
{{{ 3(-3/2)^(-2) - 7*(-3/2)^(-1) - 6 = 0 }}}
{{{ 3*(4/9)  + 7*(2/3) - 6 = 0 }}}
{{{ 3*(4/9) + 7*(6/9) - 54/9 = 0 }}}
{{{ (1/9)*( 12 + 42 - 54 ) = 0 }}}
{{{ (1/9)*( 54 - 54 ) = 0 }}}
OK