x-5/x-6=2/x

Solution for x-5/x-6=2/x equation:

x-5/x-6=2/x

We move all terms to the left:

x-5/x-6-(2/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-5/x-(+2/x)-6=0

We get rid of parentheses

x-5/x-2/x-6=0

We multiply all the terms by the denominator


x*x-6*x-5-2=0

We add all the numbers together, and all the variables

-6x+x*x-7=0

Wy multiply elements

x^2-6x-7=0

a = 1; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·1·(-7)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8}{2*1}=\frac{14}{2}
=7
$