SOLUTION: -6z^2+7z+3=0

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Question 156974: -6z^2+7z+3=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-6z%5E2%2B7z%2B3=0 Start with the given equation.


Notice we have a quadratic equation in the form of az%5E2%2Bbz%2Bc where a=-6, b=7, and c=3


Let's use the quadratic formula to solve for z


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


z+=+%28-%287%29+%2B-+sqrt%28+%287%29%5E2-4%28-6%29%283%29+%29%29%2F%282%28-6%29%29 Plug in a=-6, b=7, and c=3


z+=+%28-7+%2B-+sqrt%28+49-4%28-6%29%283%29+%29%29%2F%282%28-6%29%29 Square 7 to get 49.


z+=+%28-7+%2B-+sqrt%28+49--72+%29%29%2F%282%28-6%29%29 Multiply 4%28-6%29%283%29 to get -72


z+=+%28-7+%2B-+sqrt%28+49%2B72+%29%29%2F%282%28-6%29%29 Rewrite sqrt%2849--72%29 as sqrt%2849%2B72%29


z+=+%28-7+%2B-+sqrt%28+121+%29%29%2F%282%28-6%29%29 Add 49 to 72 to get 121


z+=+%28-7+%2B-+sqrt%28+121+%29%29%2F%28-12%29 Multiply 2 and -6 to get -12.


z+=+%28-7+%2B-+11%29%2F%28-12%29 Take the square root of 121 to get 11.


z+=+%28-7+%2B+11%29%2F%28-12%29 or z+=+%28-7+-+11%29%2F%28-12%29 Break up the expression.


z+=+%284%29%2F%28-12%29 or z+=++%28-18%29%2F%28-12%29 Combine like terms.


z+=+-1%2F3 or z+=+3%2F2 Simplify.


So the answers are z+=+-1%2F3 or z+=+3%2F2