Question 947603
{{{ 3x^2 + x - 2 }}}
Use quadratic formula
{{{ x = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 3 }}}
{{{ b = 1 }}}
{{{ c = -2 }}}
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{{{ x = ( -1 +- sqrt( 1^2 - 4*3*(-2) )) / (2*3) }}}
{{{ x = ( -1 +- sqrt( 1 + 24)) / 6 }}}
{{{ x = ( -1 +- sqrt( 25)) / 6 }}}
{{{ x = ( -1 + 5 ) / 6 }}}
{{{ x = 4/6 }}}
{{{ x = 2/3 }}}
and, using the negative square root,
{{{ x = ( -1 - 5 ) / 6 }}}
{{{ x = -6/6 }}}
{{{ x = -1 }}}
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check:
The factors are:
{{{ ( x - 2/3 )*( x + 1 ) = 0 }}}
{{{ x^2 + (1/3)*x - 2/3 = 0 }}}
Multiply both sides by {{{ 3 }}}
{{{ 3x^2 + x - 2 = 0 }}}
OK