x+5/x-5=10

Solution for x+5/x-5=10 equation:

x+5/x-5=10

We move all terms to the left:

x+5/x-5-(10)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+5/x-15=0

We multiply all the terms by the denominator


x*x-15*x+5=0

We add all the numbers together, and all the variables

-15x+x*x+5=0

Wy multiply elements

x^2-15x+5=0

a = 1; b = -15; c = +5;
Δ = b2-4ac
Δ = -152-4·1·5
Δ = 205
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{-(-15)-\sqrt{205}}{2*1}=\frac{15-\sqrt{205}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{205}}{2*1}=\frac{15+\sqrt{205}}{2}
$