x+(10/x-9)=2

Solution for x+(10/x-9)=2 equation:

x+(10/x-9)=2

We move all terms to the left:

x+(10/x-9)-(2)=0


Domain of the equation: x-9)!=0

x∈R


We get rid of parentheses

x+10/x-9-2=0

We multiply all the terms by the denominator


x*x-9*x-2*x+10=0

We add all the numbers together, and all the variables

-11x+x*x+10=0

Wy multiply elements

x^2-11x+10=0

a = 1; b = -11; c = +10;
Δ = b2-4ac
Δ = -112-4·1·10
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-9}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+9}{2*1}=\frac{20}{2}
=10
$