2=x+10/x-11

Solution for 2=x+10/x-11 equation:

2=x+10/x-11

We move all terms to the left:

2-(x+10/x-11)=0


Domain of the equation: x-11)!=0

x∈R


We get rid of parentheses

-x-10/x+11+2=0

We multiply all the terms by the denominator


-x*x+11*x+2*x-10=0

We add all the numbers together, and all the variables

13x-x*x-10=0

Wy multiply elements

-1x^2+13x-10=0

a = -1; b = 13; c = -10;
Δ = b2-4ac
Δ = 132-4·(-1)·(-10)
Δ = 129
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{-(13)-\sqrt{129}}{2*-1}=\frac{-13-\sqrt{129}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{129}}{2*-1}=\frac{-13+\sqrt{129}}{-2}
$