SOLUTION: what are the zeroes of 5x^2-13x=-6

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Question 266899: what are the zeroes of 5x^2-13x=-6
Found 2 solutions by JBarnum, gsmani_iyer:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
5x%5E2-13x=-6
5x%5E2-13x%2B6=0 A=5 B=-13 C=6
x=2, 0.6
x-2=0 & x-0.6=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-13x%2B6+=+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=%28-13%29%5E2-4%2A5%2A6=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+49+%29%29%2F2%5C5+=+2
x%5B2%5D+=+%28-%28-13%29-sqrt%28+49+%29%29%2F2%5C5+=+0.6

Quadratic expression 5x%5E2%2B-13x%2B6 can be factored:
5x%5E2%2B-13x%2B6+=+5%28x-2%29%2A%28x-0.6%29
Again, the answer is: 2, 0.6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-13%2Ax%2B6+%29

Answer by gsmani_iyer(201) About Me  (Show Source):
You can put this solution on YOUR website!
Solution: 5x%5E2-13x=-6
= 5x%5E2-13x%2B6+=+0
= 5x%5E2-10x-3x%2B6+=+0
= 5x%28x-2%29-3%28x-2%29+=+0
= %28x-2%29%285x-3%29+=+0
Here %28x-2%29 or %285x-3%29 has to be 0
If (x-2) is zero, then, x=2.
If (5x-3) is zero, then, x = 3/5
Therefore x = {2, 3/5}.