r+6/r=-7

Solution for r+6/r=-7 equation:

r+6/r=-7

We move all terms to the left:

r+6/r-(-7)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

r+6/r+7=0

We multiply all the terms by the denominator


r*r+7*r+6=0

We add all the numbers together, and all the variables

7r+r*r+6=0

Wy multiply elements

r^2+7r+6=0

a = 1; b = 7; c = +6;
Δ = b2-4ac
Δ = 72-4·1·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*1}=\frac{-12}{2}
=-6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*1}=\frac{-2}{2}
=-1
$