x-10/x=99/x+10

Solution for x-10/x=99/x+10 equation:

x-10/x=99/x+10

We move all terms to the left:

x-10/x-(99/x+10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+10)!=0

x∈R


We get rid of parentheses

x-10/x-99/x-10=0

We multiply all the terms by the denominator


x*x-10*x-10-99=0

We add all the numbers together, and all the variables

-10x+x*x-109=0

Wy multiply elements

x^2-10x-109=0

a = 1; b = -10; c = -109;
Δ = b2-4ac
Δ = -102-4·1·(-109)
Δ = 536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{536}=\sqrt{4*134}=\sqrt{4}*\sqrt{134}=2\sqrt{134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{134}}{2*1}=\frac{10-2\sqrt{134}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{134}}{2*1}=\frac{10+2\sqrt{134}}{2}
$