SOLUTION: Solve using square and diamond or quadratic equation {{{ 20x^2-30x=2x+45 }}}

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Question 853650: Solve using square and diamond or quadratic equation
+20x%5E2-30x=2x%2B45+
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
+20x%5E2-30x=2x%2B45+
Add -2x to each side
+20x%5E2-32x=45+
Add -45 to each side
+20x%5E2-32x-45=0+
Below is the quadratic solution.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 20x%5E2%2B-32x%2B-45+=+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=%28-32%29%5E2-4%2A20%2A-45=4624.

Discriminant d=4624 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--32%2B-sqrt%28+4624+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-32%29%2Bsqrt%28+4624+%29%29%2F2%5C20+=+2.5
x%5B2%5D+=+%28-%28-32%29-sqrt%28+4624+%29%29%2F2%5C20+=+-0.9

Quadratic expression 20x%5E2%2B-32x%2B-45 can be factored:
20x%5E2%2B-32x%2B-45+=+20%28x-2.5%29%2A%28x--0.9%29
Again, the answer is: 2.5, -0.9. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+20%2Ax%5E2%2B-32%2Ax%2B-45+%29