(D^2+7D+12)y=0

Solution for (D^2+7D+12)y=0 equation:

(^2+7+12)D=0

We multiply parentheses

D^2+7D+12D=0

We add all the numbers together, and all the variables

D^2+19D=0

a = 1; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·1·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*1}=\frac{-38}{2}
=-19
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*1}=\frac{0}{2}
=0
$