r^2+11r=-17

Solution for r^2+11r=-17 equation:

r^2+11r=-17

We move all terms to the left:

r^2+11r-(-17)=0

We add all the numbers together, and all the variables

r^2+11r+17=0

a = 1; b = 11; c = +17;
Δ = b2-4ac
Δ = 112-4·1·17
Δ = 53
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{53}}{2*1}=\frac{-11-\sqrt{53}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{53}}{2*1}=\frac{-11+\sqrt{53}}{2}
$