9r^2+21r+9=-r^2

Solution for 9r^2+21r+9=-r^2 equation:

9r^2+21r+9=-r^2

We move all terms to the left:

9r^2+21r+9-(-r^2)=0

We get rid of parentheses

9r^2+r^2+21r+9=0

We add all the numbers together, and all the variables

10r^2+21r+9=0

a = 10; b = 21; c = +9;
Δ = b2-4ac
Δ = 212-4·10·9
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{-(21)-9}{2*10}=\frac{-30}{20}
=-1+1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+9}{2*10}=\frac{-12}{20}
=-3/5
$