(D^2-6D+9)y=12

Solution for (D^2-6D+9)y=12 equation:

(^2-6+9)D=12

We move all terms to the left:

(^2-6+9)D-(12)=0

We multiply parentheses

D^2-6D+9D-12=0

We add all the numbers together, and all the variables

D^2+3D-12=0

a = 1; b = 3; c = -12;
Δ = b2-4ac
Δ = 32-4·1·(-12)
Δ = 57
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{-(3)-\sqrt{57}}{2*1}=\frac{-3-\sqrt{57}}{2}
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*1}=\frac{-3+\sqrt{57}}{2}
$