r^2=-6r-8

Solution for r^2=-6r-8 equation:

r^2=-6r-8

We move all terms to the left:

r^2-(-6r-8)=0

We get rid of parentheses

r^2+6r+8=0

a = 1; b = 6; c = +8;
Δ = b2-4ac
Δ = 62-4·1·8
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{-(6)-2}{2*1}=\frac{-8}{2}
=-4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2}{2*1}=\frac{-4}{2}
=-2
$