u+18/u=-11

Solution for u+18/u=-11 equation:

u+18/u=-11

We move all terms to the left:

u+18/u-(-11)=0


Domain of the equation: u!=0

u∈R


We add all the numbers together, and all the variables

u+18/u+11=0

We multiply all the terms by the denominator


u*u+11*u+18=0

We add all the numbers together, and all the variables

11u+u*u+18=0

Wy multiply elements

u^2+11u+18=0

a = 1; b = 11; c = +18;
Δ = b2-4ac
Δ = 112-4·1·18
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7}{2*1}=\frac{-18}{2}
=-9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7}{2*1}=\frac{-4}{2}
=-2
$