24/(x-5)+24/x=11

Solution for 24/(x-5)+24/x=11 equation:

24/(x-5)+24/x=11

We move all terms to the left:

24/(x-5)+24/x-(11)=0


Domain of the equation: (x-5)!=0

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

x!=5

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


24x/(x^2-5x)+(24x-120)/(x^2-5x)-11=0

We multiply all the terms by the denominator


24x+(24x-120)-11*(x^2-5x)=0

We multiply parentheses

-11x^2+24x+(24x-120)+55x=0

We get rid of parentheses

-11x^2+24x+24x+55x-120=0

We add all the numbers together, and all the variables

-11x^2+103x-120=0

a = -11; b = 103; c = -120;
Δ = b2-4ac
Δ = 1032-4·(-11)·(-120)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(103)-73}{2*-11}=\frac{-176}{-22}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(103)+73}{2*-11}=\frac{-30}{-22}
=1+4/11
$