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Let's do one we've done before so we'll recognize the answers when we get them:

2x^2 - 5x - 3 = 0

a = 2 , b = -5 , c = -3

Let's plug the stuff into our formula:

x = -b +/- sqrt( b^2 - 4ac ) / 2a = - ( -5 ) +/- sqrt( ( -5 )^2 - 4 ( 2 ) ( -3 ) ) / ( 2 ( 2 ) ) = 5 +/- sqrt( 25 + 24 ) / 4 = 5 +/- sqrt( 49 ) / 4 = 5 +/- 7 / 4 ... the +/- is how we'll get our two answers!

One with the - :

x = ( 5 - 7 ) / 4 = -2 / 4 = -1/2

   One with the + :

  x = ( 5 + 7 ) / 4 = 12 / 4 = 3

{ -1/2 , 3 }

Hey, this is what we got before by factoring!  So, this quadranator thing really works -- cool!


TRY IT:

Solve  60x^2 + 317x - 161 = 0