SOLUTION: 3x(x-3)=2x(x+2)+6, so far I've got 3x^2-9x-2x^2-4x-6=0, then x^2-13x-6=0 but after this I'm lost?

Algebra ->  Test -> SOLUTION: 3x(x-3)=2x(x+2)+6, so far I've got 3x^2-9x-2x^2-4x-6=0, then x^2-13x-6=0 but after this I'm lost?      Log On


   

Question 602851: 3x(x-3)=2x(x+2)+6, so far I've got 3x^2-9x-2x^2-4x-6=0, then x^2-13x-6=0 but after this I'm lost?
Found 2 solutions by Alan3354, flame8855:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3x(x-3)=2x(x+2)+6, so far I've got 3x^2-9x-2x^2-4x-6=0, then x^2-13x-6=0 but after this I'm lost?
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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 1x%5E2%2B-13x%2B-6+=+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=%28-13%29%5E2-4%2A1%2A-6=193.

Discriminant d=193 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+193+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+193+%29%29%2F2%5C1+=+13.4462219947249
x%5B2%5D+=+%28-%28-13%29-sqrt%28+193+%29%29%2F2%5C1+=+-0.446221994724902

Quadratic expression 1x%5E2%2B-13x%2B-6 can be factored:
1x%5E2%2B-13x%2B-6+=+%28x-13.4462219947249%29%2A%28x--0.446221994724902%29
Again, the answer is: 13.4462219947249, -0.446221994724902. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-13%2Ax%2B-6+%29

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You can do it by completing the square, also.

Answer by flame8855(424) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-13x-6=0 a = 1 , b= -13 , c = -6
delta = b^2-4ac = 169+24=193
x1= -b+delta^2/2a = (13+193^1/2) /2
x2= -b-delta^2/2a = (13-193^1/2) /2