SOLUTION: solve using the quadratic formula 2/3 x^2 - x = 5/2

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Question 200963This question is from textbook Beginning Algebra
: solve using the quadratic formula
2/3 x^2 - x = 5/2 This question is from textbook Beginning Algebra

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2/3 x^2 - x = 5/2
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Multiply by 6 to eliminate fractions
4x^2 - 6x = 15
4x^2 - 6x - 15 = 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-6x%2B-15+=+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=%28-6%29%5E2-4%2A4%2A-15=276.

Discriminant d=276 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+276+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+276+%29%29%2F2%5C4+=+2.82665596572952
x%5B2%5D+=+%28-%28-6%29-sqrt%28+276+%29%29%2F2%5C4+=+-1.32665596572952

Quadratic expression 4x%5E2%2B-6x%2B-15 can be factored:
4x%5E2%2B-6x%2B-15+=+%28x-2.82665596572952%29%2A%28x--1.32665596572952%29
Again, the answer is: 2.82665596572952, -1.32665596572952. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-6%2Ax%2B-15+%29

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The solver doesn't get the factors right when the coeff of the x^2 term is not 1, so ignore that, and ignore what it says for factors.
x = (3 + sqrt(69))/4
x = (3 - sqrt(69))/4