SOLUTION: Find all real solutions of the quadratic equation. (10y)square - 16y + 5 = 0

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Question 45428: Find all real solutions of the quadratic equation.
(10y)square - 16y + 5 = 0
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
10y^2 - 16y + 5 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 10y%5E2%2B-16y%2B5+=+0) has the following solutons:

y%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=%28-16%29%5E2-4%2A10%2A5=56.

Discriminant d=56 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+56+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+56+%29%29%2F2%5C10+=+1.17416573867739
y%5B2%5D+=+%28-%28-16%29-sqrt%28+56+%29%29%2F2%5C10+=+0.425834261322606

Quadratic expression 10y%5E2%2B-16y%2B5 can be factored:
10y%5E2%2B-16y%2B5+=+10%28y-1.17416573867739%29%2A%28y-0.425834261322606%29
Again, the answer is: 1.17416573867739, 0.425834261322606. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B-16%2Ax%2B5+%29