X+8/x=-6

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

X+8/X=-6

We move all terms to the left:

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