SOLUTION: solve the equation 52x-4x^2=60

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Question 280327: solve the equation 52x-4x^2=60
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
solve the equation 52x-4x^2=60
.
Reordering:
0 = 4x^2 - 52x + 60
Dividing both sides by 4:
0 = x^2 - 13x + 15
Since we can't factor we must resort to the quadratic equation.
Doing so yields:
x = {11.72, 1.28}
.
Details of quadratic:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-13x%2B15+=+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%2A1%2A15=109.

Discriminant d=109 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+109+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+109+%29%29%2F2%5C1+=+11.7201532544553
x%5B2%5D+=+%28-%28-13%29-sqrt%28+109+%29%29%2F2%5C1+=+1.27984674554472

Quadratic expression 1x%5E2%2B-13x%2B15 can be factored:
1x%5E2%2B-13x%2B15+=+1%28x-11.7201532544553%29%2A%28x-1.27984674554472%29
Again, the answer is: 11.7201532544553, 1.27984674554472. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-13%2Ax%2B15+%29