SOLUTION: Use quadratic formula and a calculator to solve. Round decimal approximations to the nearest hundredth. 2/3x^2 - 4/5x - 1/2 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Use quadratic formula and a calculator to solve. Round decimal approximations to the nearest hundredth. 2/3x^2 - 4/5x - 1/2 = 0      Log On


   

Question 1029170: Use quadratic formula and a calculator to solve. Round decimal approximations to the nearest hundredth.
2/3x^2 - 4/5x - 1/2 = 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2/3x^2 - 4/5x - 1/2 = 0
20x^2 - 24x - 15 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 20x%5E2%2B-24x%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=%28-24%29%5E2-4%2A20%2A-15=1776.

Discriminant d=1776 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--24%2B-sqrt%28+1776+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-24%29%2Bsqrt%28+1776+%29%29%2F2%5C20+=+1.65356537528527
x%5B2%5D+=+%28-%28-24%29-sqrt%28+1776+%29%29%2F2%5C20+=+-0.453565375285274

Quadratic expression 20x%5E2%2B-24x%2B-15 can be factored:
20x%5E2%2B-24x%2B-15+=+%28x-1.65356537528527%29%2A%28x--0.453565375285274%29
Again, the answer is: 1.65356537528527, -0.453565375285274. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+20%2Ax%5E2%2B-24%2Ax%2B-15+%29