(D^2+5D+6)y=3

Solution for (D^2+5D+6)y=3 equation:

(^2+5+6)D=3

We move all terms to the left:

(^2+5+6)D-(3)=0

We multiply parentheses

D^2+5D+6D-3=0

We add all the numbers together, and all the variables

D^2+11D-3=0

a = 1; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·1·(-3)
Δ = 133
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{133}}{2*1}=\frac{-11-\sqrt{133}}{2}
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{133}}{2*1}=\frac{-11+\sqrt{133}}{2}
$