2=x+6/x-9

Solution for 2=x+6/x-9 equation:

2=x+6/x-9

We move all terms to the left:

2-(x+6/x-9)=0


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

x∈R


We get rid of parentheses

-x-6/x+9+2=0

We multiply all the terms by the denominator


-x*x+9*x+2*x-6=0

We add all the numbers together, and all the variables

11x-x*x-6=0

Wy multiply elements

-1x^2+11x-6=0

a = -1; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·(-1)·(-6)
Δ = 97
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{-(11)-\sqrt{97}}{2*-1}=\frac{-11-\sqrt{97}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{97}}{2*-1}=\frac{-11+\sqrt{97}}{-2}
$