SOLUTION: Solve the followong equations or inequalities: 6x^2 +7x=5

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Question 173637: Solve the followong equations or inequalities:
6x^2 +7x=5
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
6x%5E2%2B7x-5=0
:
you have 2 choices for the squared term when factoring this
6 and 1
3 and 2
:
you have 1 choice for the constant
:
5 and 1:
:
since the constant is -5 then we will have one positive and one negative middle term . such as 6(5)-1(1) or 3(5)-2(1)
:
through process of elimination we get: 2(5)-3(1)=7(our middle term)
:
If none of these had worked we would have had to use the quadratic formula
:
%283x%2B5%29%282x-1%29as the factors
:
3x+5=0--->3x=-5--->x=-5/3
:
2x-1=0--->2x=1--->x=1/2
:
system%28x=-5%2F3%2Cx=1%2F2%29
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B7x%2B-5+=+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=%287%29%5E2-4%2A6%2A-5=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+169+%29%29%2F2%5C6+=+0.5
x%5B2%5D+=+%28-%287%29-sqrt%28+169+%29%29%2F2%5C6+=+-1.66666666666667

Quadratic expression 6x%5E2%2B7x%2B-5 can be factored:
6x%5E2%2B7x%2B-5+=+%28x-0.5%29%2A%28x--1.66666666666667%29
Again, the answer is: 0.5, -1.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B7%2Ax%2B-5+%29