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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=276 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2.82665596572952, -1.32665596572952. Here's your graph:

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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

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