2x-6/x-6=x/x+2

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

2x-6/x-6=x/x+2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

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

Fractions to decimals

-6/x+2x-2-6+1=0

We multiply all the terms by the denominator


2x*x-2*x-6*x+1*x-6=0

We add all the numbers together, and all the variables

-7x+2x*x-6=0

Wy multiply elements

2x^2-7x-6=0

a = 2; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·2·(-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{-(-7)-\sqrt{97}}{2*2}=\frac{7-\sqrt{97}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*2}=\frac{7+\sqrt{97}}{4}
$