720/(x-6)-720/x=6

Solution for 720/(x-6)-720/x=6 equation:

720/(x-6)-720/x=6

We move all terms to the left:

720/(x-6)-720/x-(6)=0


Domain of the equation: (x-6)!=0

We move all terms containing x to the left, all other terms to the right

x!=6

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


720x/(x^2-6x)+(-720x+4320)/(x^2-6x)-6=0

We multiply all the terms by the denominator


720x+(-720x+4320)-6*(x^2-6x)=0

We multiply parentheses

-6x^2+720x+(-720x+4320)+36x=0

We get rid of parentheses

-6x^2+720x-720x+36x+4320=0

We add all the numbers together, and all the variables

-6x^2+36x+4320=0

a = -6; b = 36; c = +4320;
Δ = b2-4ac
Δ = 362-4·(-6)·4320
Δ = 104976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{104976}=324$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-324}{2*-6}=\frac{-360}{-12}
=+30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+324}{2*-6}=\frac{288}{-12}
=-24
$