x+2/X-8=6

Solution for x+2/X-8=6 equation:

x+2/x-8=6

We move all terms to the left:

x+2/x-8-(6)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+2/x-14=0

We multiply all the terms by the denominator


x*x-14*x+2=0

We add all the numbers together, and all the variables

-14x+x*x+2=0

Wy multiply elements

x^2-14x+2=0

a = 1; b = -14; c = +2;
Δ = b2-4ac
Δ = -142-4·1·2
Δ = 188
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{47}}{2*1}=\frac{14-2\sqrt{47}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{47}}{2*1}=\frac{14+2\sqrt{47}}{2}
$