SOLUTION: This problem is 8x squared minus 3 equals 10x or 8x^2-3=10x Then it says solve. Please help. Thank you. I feel like I should get everything on one side and set it to 0 but, from

Algebra ->  Equations -> SOLUTION: This problem is 8x squared minus 3 equals 10x or 8x^2-3=10x Then it says solve. Please help. Thank you. I feel like I should get everything on one side and set it to 0 but, from       Log On


   

Question 601453: This problem is 8x squared minus 3 equals 10x or 8x^2-3=10x
Then it says solve. Please help. Thank you. I feel like I should get everything on one side and set it to 0 but, from there on I'm not sure what to do.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is 8x squared minus 3 equals 10x or 8x^2-3=10x
Then it says solve. Please help. Thank you. I feel like I should get everything on one side and set it to 0 but, from there on I'm not sure what to do.
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That is step 1.
8x%5E2+-+10x+-+3+=+0
Then you can factor it.
(2x - 3)*(4x + 1) = 0
-----
2x-3 = 0
x = 3/2
-----
4x+1 = 0
x = -1/4
==========
If it can't be factored, use the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B-10x%2B-3+=+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=%28-10%29%5E2-4%2A8%2A-3=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+196+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+196+%29%29%2F2%5C8+=+1.5
x%5B2%5D+=+%28-%28-10%29-sqrt%28+196+%29%29%2F2%5C8+=+-0.25

Quadratic expression 8x%5E2%2B-10x%2B-3 can be factored:
8x%5E2%2B-10x%2B-3+=+%28x-1.5%29%2A%28x--0.25%29
Again, the answer is: 1.5, -0.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-10%2Ax%2B-3+%29