SOLUTION: 3w^2+13w=10

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Question 265121: 3w^2+13w=10
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
3w%5E2%2B13w=10
3w%5E2%2B13w-10=0 Use quadratic formula Ax%5E2%2BBx%2BC=0 A=3 B=13 C=-10
the answer is: 0.666666666666667, -5 Follow solver below
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case 3w%5E2%2B13w%2B-10+=+0) has the following solutons:

w%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=%2813%29%5E2-4%2A3%2A-10=289.

Discriminant d=289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-13%2B-sqrt%28+289+%29%29%2F2%5Ca.

w%5B1%5D+=+%28-%2813%29%2Bsqrt%28+289+%29%29%2F2%5C3+=+0.666666666666667
w%5B2%5D+=+%28-%2813%29-sqrt%28+289+%29%29%2F2%5C3+=+-5

Quadratic expression 3w%5E2%2B13w%2B-10 can be factored:
3w%5E2%2B13w%2B-10+=+3%28w-0.666666666666667%29%2A%28w--5%29
Again, the answer is: 0.666666666666667, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B13%2Ax%2B-10+%29