SOLUTION: 3x^2+14x-24=0

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Question 242738: 3x^2+14x-24=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2%2B14x-24=0 Start with the given equation.


Notice that the quadratic 3x%5E2%2B14x-24 is in the form of Ax%5E2%2BBx%2BC where A=3, B=14, and C=-24


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-%2814%29+%2B-+sqrt%28+%2814%29%5E2-4%283%29%28-24%29+%29%29%2F%282%283%29%29 Plug in A=3, B=14, and C=-24


x+=+%28-14+%2B-+sqrt%28+196-4%283%29%28-24%29+%29%29%2F%282%283%29%29 Square 14 to get 196.


x+=+%28-14+%2B-+sqrt%28+196--288+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-24%29 to get -288


x+=+%28-14+%2B-+sqrt%28+196%2B288+%29%29%2F%282%283%29%29 Rewrite sqrt%28196--288%29 as sqrt%28196%2B288%29


x+=+%28-14+%2B-+sqrt%28+484+%29%29%2F%282%283%29%29 Add 196 to 288 to get 484


x+=+%28-14+%2B-+sqrt%28+484+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-14+%2B-+22%29%2F%286%29 Take the square root of 484 to get 22.


x+=+%28-14+%2B+22%29%2F%286%29 or x+=+%28-14+-+22%29%2F%286%29 Break up the expression.


x+=+%288%29%2F%286%29 or x+=++%28-36%29%2F%286%29 Combine like terms.


x+=+4%2F3 or x+=+-6 Simplify.


So the solutions are x+=+4%2F3 or x+=+-6