SOLUTION: Please me help to solve this equation? {{{y=2x^2+4x-3}}}

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Question 1044117: Please me help to solve this equation?
y=2x%5E2%2B4x-3
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
y=2x%5E%2B4x-3
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%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=%284%29%5E2-4%2A2%2A-3=40.

Discriminant d=40 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+40+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+40+%29%29%2F2%5C2+=+0.58113883008419
x%5B2%5D+=+%28-%284%29-sqrt%28+40+%29%29%2F2%5C2+=+-2.58113883008419

Quadratic expression 2x%5E2%2B4x%2B-3 can be factored:
2x%5E2%2B4x%2B-3+=+%28x-0.58113883008419%29%2A%28x--2.58113883008419%29
Again, the answer is: 0.58113883008419, -2.58113883008419. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-3+%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y=2x%5E2%2B4x-3.....use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ....since you have a=2, b=4, and c=-3, you will have
x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A2%2A%28-3%29+%29%29%2F%282%2A2%29+
x+=+%28-4+%2B-+sqrt%28+16%2B24+%29%29%2F4+
x+=+%28-4+%2B-+sqrt%28+40+%29%29%2F4+
x+=+%28-4+%2B-+sqrt%28+4%2A10+%29%29%2F4+
x+=+%28-4+%2B-+2sqrt%28+10+%29%29%2F4+ ...simplify

x+=+%28-cross%284%292+%2B-+cross%282%29sqrt%28+10+%29%29%2Fcross%284%292+

x+=+%28-2+%2B-+sqrt%28+10+%29%29%2F2+
x+=+%28-2%2F2+%2B-+sqrt%28+10+%29%2F2%29+
x+=+%28-1+%2B-+sqrt%28+10+%29%2F2%29+
exact solutions:
x+=++sqrt%28+10+%29%2F2-1+
x+=+-1+-+sqrt%28+10+%29%2F2+
approximate solutions:
x+=++0.58+
x+=+-2.58+