SOLUTION: If six times the square of a number is diminished by ten times the number, the result it 304. What is the number? what i tried to work out-- 6n2 -10n-304= 0 then i tried to u

Algebra ->  Expressions-with-variables -> SOLUTION: If six times the square of a number is diminished by ten times the number, the result it 304. What is the number? what i tried to work out-- 6n2 -10n-304= 0 then i tried to u      Log On


   

Question 599889: If six times the square of a number is diminished by ten times the number, the result it 304. What is the number?
what i tried to work out--
6n2 -10n-304= 0
then i tried to use the quadratic equation, but im not sure if it is right..
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If six times the square of a number is diminished by ten times the number, the result it 304. What is the number?
what i tried to work out--
6n2 -10n-304= 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-10x%2B-304+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-10%29%5E2-4%2A6%2A-304=7396.

Discriminant d=7396 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+7396+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+7396+%29%29%2F2%5C6+=+8
x%5B2%5D+=+%28-%28-10%29-sqrt%28+7396+%29%29%2F2%5C6+=+-6.33333333333333

Quadratic expression 6x%5E2%2B-10x%2B-304 can be factored:
6x%5E2%2B-10x%2B-304+=+%28x-8%29%2A%28x--6.33333333333333%29
Again, the answer is: 8, -6.33333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-10%2Ax%2B-304+%29

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