Question 1037594
There can be 0, 1, or 2 real solution
If the discriminant {{{ b^2 - 4*a*c }}} is positive, 
then the solutions are real
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{{{ a = 7 }}}
{{{ b = 14 }}}
{{{ c = -5 }}}
{{{ b^2 - 4*a*c = 14^2 - 4*7*(-5) }}}
{{{ b^2 - 4*a*c = 196 + 140 }}}
{{{ b^2 - 4*a*c = 336 }}}
The solutions are real
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Use the quadratic formula:
{{{ x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ x = (-14 +- sqrt( 14^2-4*7*(-5) ))/(2*7) }}}
{{{ x = (-14 +- sqrt( 336 ))/14 }}}
{{{ x = ( -14 + 18.3303 ) / 14 }}}
{{{ x = 4.3303 / 14 }}}
{{{ x = .3093 }}}
and
{{{ x = ( -14 - 18.3303 ) / 14 }}}
{{{ x = -32.3303 / 14 }}}
{{{ x = -2.3093 }}}
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Here's the plot:
{{{ graph( 400, 400, -5, 5, -15, 15, 7x^2 + 14x - 5 ) }}}