y+(30)/(y)=-11

Solution for y+(30)/(y)=-11 equation:

y+(30)/(y)=-11

We move all terms to the left:

y+(30)/(y)-(-11)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

y+30/y+11=0

We multiply all the terms by the denominator


y*y+11*y+30=0

We add all the numbers together, and all the variables

11y+y*y+30=0

Wy multiply elements

y^2+11y+30=0

a = 1; b = 11; c = +30;
Δ = b2-4ac
Δ = 112-4·1·30
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-1}{2*1}=\frac{-12}{2}
=-6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+1}{2*1}=\frac{-10}{2}
=-5
$