SOLUTION: s^2=3 +s(1-4s) solve the given quadratic equation , using the quadratic formula?

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Question 632503: s^2=3 +s(1-4s)
solve the given quadratic equation , using the quadratic formula?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!

First let's put it in normal quadratic order.
s^2=3 +s(1-4s) becomes
s2=3+s-4s^2
5s^2-s-3=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-1x%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=%28-1%29%5E2-4%2A5%2A-3=61.

Discriminant d=61 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+61+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+61+%29%29%2F2%5C5+=+0.881024967590665
x%5B2%5D+=+%28-%28-1%29-sqrt%28+61+%29%29%2F2%5C5+=+-0.681024967590665

Quadratic expression 5x%5E2%2B-1x%2B-3 can be factored:
5x%5E2%2B-1x%2B-3+=+5%28x-0.881024967590665%29%2A%28x--0.681024967590665%29
Again, the answer is: 0.881024967590665, -0.681024967590665. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-1%2Ax%2B-3+%29