X+14/x=-9

Solution for X+14/x=-9 equation:

X+14/X=-9

We move all terms to the left:

X+14/X-(-9)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+14/X+9=0

We multiply all the terms by the denominator


X*X+9*X+14=0

We add all the numbers together, and all the variables

9X+X*X+14=0

Wy multiply elements

X^2+9X+14=0

a = 1; b = 9; c = +14;
Δ = b2-4ac
Δ = 92-4·1·14
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{-(9)-5}{2*1}=\frac{-14}{2}
=-7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5}{2*1}=\frac{-4}{2}
=-2
$