x+18/x=-9

Solution for x+18/x=-9 equation:

x+18/x=-9

We move all terms to the left:

x+18/x-(-9)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+18/x+9=0

We multiply all the terms by the denominator


x*x+9*x+18=0

We add all the numbers together, and all the variables

9x+x*x+18=0

Wy multiply elements

x^2+9x+18=0

a = 1; b = 9; c = +18;
Δ = b2-4ac
Δ = 92-4·1·18
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*1}=\frac{-6}{2}
=-3
$