r^2+8=-9r

Solution for r^2+8=-9r equation:

r^2+8=-9r

We move all terms to the left:

r^2+8-(-9r)=0

We get rid of parentheses

r^2+9r+8=0

a = 1; b = 9; c = +8;
Δ = b2-4ac
Δ = 92-4·1·8
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7}{2*1}=\frac{-16}{2}
=-8
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7}{2*1}=\frac{-2}{2}
=-1
$