r+3/r=-4

Solution for r+3/r=-4 equation:

r+3/r=-4

We move all terms to the left:

r+3/r-(-4)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

r+3/r+4=0

We multiply all the terms by the denominator


r*r+4*r+3=0

We add all the numbers together, and all the variables

4r+r*r+3=0

Wy multiply elements

r^2+4r+3=0

a = 1; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·1·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2}{2*1}=\frac{-6}{2}
=-3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2}{2*1}=\frac{-2}{2}
=-1
$