11r+15=-r^2

Solution for 11r+15=-r^2 equation:

11r+15=-r^2

We move all terms to the left:

11r+15-(-r^2)=0

We get rid of parentheses

r^2+11r+15=0

a = 1; b = 11; c = +15;
Δ = b2-4ac
Δ = 112-4·1·15
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{61}}{2*1}=\frac{-11-\sqrt{61}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{61}}{2*1}=\frac{-11+\sqrt{61}}{2}
$