u+18/u=-9

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

u+18/u=-9

We move all terms to the left:

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


Domain of the equation: u!=0

u∈R


We add all the numbers together, and all the variables

u+18/u+9=0

We multiply all the terms by the denominator


u*u+9*u+18=0

We add all the numbers together, and all the variables

9u+u*u+18=0

Wy multiply elements

u^2+9u+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:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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