SOLUTION: 3y^2=y+10

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Question 670045: 3y^2=y+10
Found 2 solutions by ReadingBoosters, vleith:
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
3y%5E2+-+y+-+10
...
(3y+5)(y-2)
y = -5%2F3
y = 2
.....................
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Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
3y%5E2=y%2B10
3y%5E2+-+y+-+10+=+0
%283y+%2B+5%29%28y-2%29+=+0
So either %283y+%2B+5%29=0 or %28y-2%29=0
Solve each of those for y to find the possible solutions
y = -5/3 or 2
You cna also use the quadratic formula to get the same answer
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-1x%2B-10+=+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=%28-1%29%5E2-4%2A3%2A-10=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+121+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+121+%29%29%2F2%5C3+=+2
x%5B2%5D+=+%28-%28-1%29-sqrt%28+121+%29%29%2F2%5C3+=+-1.66666666666667

Quadratic expression 3x%5E2%2B-1x%2B-10 can be factored:
3x%5E2%2B-1x%2B-10+=+3%28x-2%29%2A%28x--1.66666666666667%29
Again, the answer is: 2, -1.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-1%2Ax%2B-10+%29