SOLUTION: Solve 6x^2+3x-18=0 using the quadratic formula

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Question 156350: Solve 6x^2+3x-18=0 using the quadratic formula
Found 2 solutions by oscargut, jim_thompson5910:
Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!
6x^2+3x-18=0
x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A6%2A%28-18%29+%29%29%2F%282%2A6%29+=
x+=+%28-3+%2B-+sqrt%28441%29%29%2F12+=
x+=+%28-3+%2B-+21%29%2F12+
so roots are: 18%2F12=3%2F2 and x=-24%2F12=-2
Answer: x=3%2F2,x=-2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6x%5E2%2B3x-18=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=6, b=3, and c=-18


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-%283%29+%2B-+sqrt%28+%283%29%5E2-4%286%29%28-18%29+%29%29%2F%282%286%29%29 Plug in a=6, b=3, and c=-18


x+=+%28-3+%2B-+sqrt%28+9-4%286%29%28-18%29+%29%29%2F%282%286%29%29 Square 3 to get 9.


x+=+%28-3+%2B-+sqrt%28+9--432+%29%29%2F%282%286%29%29 Multiply 4%286%29%28-18%29 to get -432


x+=+%28-3+%2B-+sqrt%28+9%2B432+%29%29%2F%282%286%29%29 Rewrite sqrt%289--432%29 as sqrt%289%2B432%29


x+=+%28-3+%2B-+sqrt%28+441+%29%29%2F%282%286%29%29 Add 9 to 432 to get 441


x+=+%28-3+%2B-+sqrt%28+441+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%28-3+%2B-+21%29%2F%2812%29 Take the square root of 441 to get 21.


x+=+%28-3+%2B+21%29%2F%2812%29 or x+=+%28-3+-+21%29%2F%2812%29 Break up the expression.


x+=+%2818%29%2F%2812%29 or x+=++%28-24%29%2F%2812%29 Combine like terms.


x+=+3%2F2 or x+=+-2 Simplify.


So the answers are x+=+3%2F2 or x+=+-2