x+30/x=-11

Solution for x+30/x=-11 equation:

x+30/x=-11

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+30/x+11=0

We multiply all the terms by the denominator


x*x+11*x+30=0

We add all the numbers together, and all the variables

11x+x*x+30=0

Wy multiply elements

x^2+11x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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