d^2+21d=-110

Solution for d^2+21d=-110 equation:

d^2+21d=-110

We move all terms to the left:

d^2+21d-(-110)=0

We add all the numbers together, and all the variables

d^2+21d+110=0

a = 1; b = 21; c = +110;
Δ = b2-4ac
Δ = 212-4·1·110
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-1}{2*1}=\frac{-22}{2}
=-11
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+1}{2*1}=\frac{-20}{2}
=-10
$