SOLUTION: 6x^2+x-2=0 sovle this equation using quadratic formula

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Question 318067: 6x^2+x-2=0 sovle this equation using quadratic formula
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6x%5E2%2Bx-2=0 Start with the given equation.


Notice that the quadratic 6x%5E2%2Bx-2 is in the form of Ax%5E2%2BBx%2BC where A=6, 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-%281%29+%2B-+sqrt%28+%281%29%5E2-4%286%29%28-2%29+%29%29%2F%282%286%29%29 Plug in A=6, B=1, and C=-2


x+=+%28-1+%2B-+sqrt%28+1-4%286%29%28-2%29+%29%29%2F%282%286%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--48+%29%29%2F%282%286%29%29 Multiply 4%286%29%28-2%29 to get -48


x+=+%28-1+%2B-+sqrt%28+1%2B48+%29%29%2F%282%286%29%29 Rewrite sqrt%281--48%29 as sqrt%281%2B48%29


x+=+%28-1+%2B-+sqrt%28+49+%29%29%2F%282%286%29%29 Add 1 to 48 to get 49


x+=+%28-1+%2B-+sqrt%28+49+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%28-1+%2B-+7%29%2F%2812%29 Take the square root of 49 to get 7.


x+=+%28-1+%2B+7%29%2F%2812%29 or x+=+%28-1+-+7%29%2F%2812%29 Break up the expression.


x+=+%286%29%2F%2812%29 or x+=++%28-8%29%2F%2812%29 Combine like terms.


x+=+1%2F2 or x+=+-2%2F3 Simplify.


So the solutions are x+=+1%2F2 or x+=+-2%2F3