SOLUTION: 5x^2-2x-3=0.find x

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Question 762611: 5x^2-2x-3=0.find x
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Equation is 5%2Ax%5E2+-+2%2Ax+-+3+=+0
We can solve it through factorization.
Any equation of the form a%2Ax%5E2+%2B+b%5Ex+%2B+c+=+0, if it has two factors f1 and f2, then f1*f2 = a*c, f1+f2 = b
5%2Ax%5E2+-+5%2Ax+%2B+3%2Ax+-+3+=+0
5%2Ax%28x+-+1%29+%2B+3%2A%28x+-+1%29+=+0
%285%2Ax+%2B+3%29%2A%28x+-+1%29+=+0
So the roots are:
5%2Ax+%2B+3+=+0 or x+=+-3%2F5
x+-+1+=+0 or x+=+1
Roots of the equation are highlight%28-3%2F5%29 and highlight%281%29
You can also solve it using the standard quadratic solution formula as described below.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-2x%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=%28-2%29%5E2-4%2A5%2A-3=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+64+%29%29%2F2%5C5+=+1
x%5B2%5D+=+%28-%28-2%29-sqrt%28+64+%29%29%2F2%5C5+=+-0.6

Quadratic expression 5x%5E2%2B-2x%2B-3 can be factored:
5x%5E2%2B-2x%2B-3+=+5%28x-1%29%2A%28x--0.6%29
Again, the answer is: 1, -0.6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-2%2Ax%2B-3+%29