SOLUTION: 3x^2 -x-2 =0 how do I solve this equation using quadratic solution...thank you very much for helping me...

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Question 171807: 3x^2 -x-2 =0 how do I solve this equation using quadratic solution...thank you very much for helping me...
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2-x-2=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=3, b=-1, and c=-2


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%283%29%28-2%29+%29%29%2F%282%283%29%29 Plug in a=3, b=-1, and c=-2


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%283%29%28-2%29+%29%29%2F%282%283%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%283%29%28-2%29+%29%29%2F%282%283%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--24+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-2%29 to get -24


x+=+%281+%2B-+sqrt%28+1%2B24+%29%29%2F%282%283%29%29 Rewrite sqrt%281--24%29 as sqrt%281%2B24%29


x+=+%281+%2B-+sqrt%28+25+%29%29%2F%282%283%29%29 Add 1 to 24 to get 25


x+=+%281+%2B-+sqrt%28+25+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%281+%2B-+5%29%2F%286%29 Take the square root of 25 to get 5.


x+=+%281+%2B+5%29%2F%286%29 or x+=+%281+-+5%29%2F%286%29 Break up the expression.


x+=+%286%29%2F%286%29 or x+=++%28-4%29%2F%286%29 Combine like terms.


x+=+1 or x+=+-2%2F3 Simplify.


So the answers are x+=+1 or x+=+-2%2F3