SOLUTION: 2x+3x^2=50

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Question 190172: 2x+3x^2=50
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2%2B2x-50=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B2x%2B-50+=+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=%282%29%5E2-4%2A3%2A-50=604.

Discriminant d=604 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+604+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+604+%29%29%2F2%5C3+=+3.7627352424815
x%5B2%5D+=+%28-%282%29-sqrt%28+604+%29%29%2F2%5C3+=+-4.42940190914817

Quadratic expression 3x%5E2%2B2x%2B-50 can be factored:
3x%5E2%2B2x%2B-50+=+%28x-3.7627352424815%29%2A%28x--4.42940190914817%29
Again, the answer is: 3.7627352424815, -4.42940190914817. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B2%2Ax%2B-50+%29