x-5/x=24/x+5

Solution for x-5/x=24/x+5 equation:

x-5/x=24/x+5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x+5)!=0

x∈R


We get rid of parentheses

x-5/x-24/x-5=0

We multiply all the terms by the denominator


x*x-5*x-5-24=0

We add all the numbers together, and all the variables

-5x+x*x-29=0

Wy multiply elements

x^2-5x-29=0

a = 1; b = -5; c = -29;
Δ = b2-4ac
Δ = -52-4·1·(-29)
Δ = 141
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{141}}{2*1}=\frac{5-\sqrt{141}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{141}}{2*1}=\frac{5+\sqrt{141}}{2}
$