Question 712761
{{{ -6=-6x^2+9x }}}
Divide both sides by {{{ -3 }}}
{{{ 2 = 2x^2 - 3x }}}
Subtract {{{ 2 }}} from both sides
{{{ 2x^2 - 3x - 2 = 0 }}}
Use the quadratic formula
{{{ x = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 2 }}}
{{{ b = -3 }}}
{{{ c = -2 }}}
{{{ x = (-(-3) +- sqrt( (-3)^2 - 4*2*(-2) )) / (2*2) }}}
{{{ x = ( 3 +- sqrt( 9 + 16)) / 4 }}}
{{{ x = ( 3 +- sqrt( 25)) / 4 }}}
{{{ x = ( 3 + 5) / 4 }}}
{{{ x = 8/4 }}}
{{{ x = 2 }}}
and, taking the negative square root,
{{{ x = ( 3 - 5) / 4 }}}
{{{ x = -2/4 }}}
{{{ x = -1/2 }}}
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check answers:
{{{ ( x - 2 )*( x + 1/2 ) = 0 }}}
{{{ x^2 - 2x + (1/2)*x - 1 = 0 }}}
{{{ x^2 -(3/2)*x - 1 = 0 }}}
{{{ -x^2 + (3/2)*x = -1 }}}
Multiply both sides by {{{ 6 }}}
{{{ -6x^2 + 9x = -6 }}}
OK