x-6/x+2=3

Solution for x-6/x+2=3 equation:

x-6/x+2=3

We move all terms to the left:

x-6/x+2-(3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-6/x-1=0

We multiply all the terms by the denominator


x*x-1*x-6=0

We add all the numbers together, and all the variables

-1x+x*x-6=0

Wy multiply elements

x^2-1x-6=0

a = 1; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·1·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*1}=\frac{6}{2}
=3
$