2=x-11/x-3

Solution for 2=x-11/x-3 equation:

2=x-11/x-3

We move all terms to the left:

2-(x-11/x-3)=0


Domain of the equation: x-3)!=0

x∈R


We get rid of parentheses

-x+11/x+3+2=0

We multiply all the terms by the denominator


-x*x+3*x+2*x+11=0

We add all the numbers together, and all the variables

5x-x*x+11=0

Wy multiply elements

-1x^2+5x+11=0

a = -1; b = 5; c = +11;
Δ = b2-4ac
Δ = 52-4·(-1)·11
Δ = 69
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{69}}{2*-1}=\frac{-5-\sqrt{69}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{69}}{2*-1}=\frac{-5+\sqrt{69}}{-2}
$