SOLUTION: -1/6x (x+3) = 1/4 (3-x)

Algebra ->  Equations -> SOLUTION: -1/6x (x+3) = 1/4 (3-x)      Log On


   

Question 987151: -1/6x (x+3) = 1/4 (3-x)
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
%28-1%2F6x%29%28x%2B3%29=%281%2F4%29%283-x%29 Multiply by 12x
%28-2%29%28x%2B3%29=%283x%29%283-x%29
-2x-6=9x-3x%5E2
0=11x%2B6-3x%5E2
3x%5E2-11x-6=0
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-11x%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=%28-11%29%5E2-4%2A3%2A-6=193.

Discriminant d=193 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+193+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+193+%29%29%2F2%5C3+=+4.1487406649083
x%5B2%5D+=+%28-%28-11%29-sqrt%28+193+%29%29%2F2%5C3+=+-0.482073998241634

Quadratic expression 3x%5E2%2B-11x%2B-6 can be factored:
3x%5E2%2B-11x%2B-6+=+3%28x-4.1487406649083%29%2A%28x--0.482073998241634%29
Again, the answer is: 4.1487406649083, -0.482073998241634. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-11%2Ax%2B-6+%29