x+8/x-4=2

Solution for x+8/x-4=2 equation:

x+8/x-4=2

We move all terms to the left:

x+8/x-4-(2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+8/x-6=0

We multiply all the terms by the denominator


x*x-6*x+8=0

We add all the numbers together, and all the variables

-6x+x*x+8=0

Wy multiply elements

x^2-6x+8=0

a = 1; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·1·8
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*1}=\frac{8}{2}
=4
$