r+10/r=-11

Solution for r+10/r=-11 equation:

r+10/r=-11

We move all terms to the left:

r+10/r-(-11)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

r+10/r+11=0

We multiply all the terms by the denominator


r*r+11*r+10=0

We add all the numbers together, and all the variables

11r+r*r+10=0

Wy multiply elements

r^2+11r+10=0

a = 1; b = 11; c = +10;
Δ = b2-4ac
Δ = 112-4·1·10
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-9}{2*1}=\frac{-20}{2}
=-10
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+9}{2*1}=\frac{-2}{2}
=-1
$