SOLUTION: Solve the quadratic equation 1/5x^2-3x+5/4=0 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

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Question 800585: Solve the quadratic equation
1/5x^2-3x+5/4=0
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the quadratic equation
1/5x^2-3x+5/4=0
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4x%5E2+-+60x+%2B+25+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-60x%2B25+=+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=%28-60%29%5E2-4%2A4%2A25=3200.

Discriminant d=3200 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--60%2B-sqrt%28+3200+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-60%29%2Bsqrt%28+3200+%29%29%2F2%5C4+=+14.5710678118655
x%5B2%5D+=+%28-%28-60%29-sqrt%28+3200+%29%29%2F2%5C4+=+0.428932188134524

Quadratic expression 4x%5E2%2B-60x%2B25 can be factored:
4x%5E2%2B-60x%2B25+=+%28x-14.5710678118655%29%2A%28x-0.428932188134524%29
Again, the answer is: 14.5710678118655, 0.428932188134524. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-60%2Ax%2B25+%29

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x = 15/2 + 5sqrt(2)
x = 15/2 - 5sqrt(2)