SOLUTION: {{{x+2/(x-3)+(x/5)=(5/(x-3))}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: {{{x+2/(x-3)+(x/5)=(5/(x-3))}}}      Log On


   

Question 309207: x%2B2%2F%28x-3%29%2B%28x%2F5%29=%285%2F%28x-3%29%29
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B2%2F%28x-3%29%2B%28x%2F5%29=%285%2F%28x-3%29%29multiply everything by ((5)(x-3))


5x%5E2-15x%2B10%2Bx%5E2-3x=25
6x%5E2-18x%2B10=25
6x%5E2-18x-15=0
3%282x%5E2-6x-5%29=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-6x%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=%28-6%29%5E2-4%2A2%2A-5=76.

Discriminant d=76 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+76+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+76+%29%29%2F2%5C2+=+3.67944947177034
x%5B2%5D+=+%28-%28-6%29-sqrt%28+76+%29%29%2F2%5C2+=+-0.679449471770337

Quadratic expression 2x%5E2%2B-6x%2B-5 can be factored:
2x%5E2%2B-6x%2B-5+=+2%28x-3.67944947177034%29%2A%28x--0.679449471770337%29
Again, the answer is: 3.67944947177034, -0.679449471770337. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-6%2Ax%2B-5+%29