(D^2-5D+6)y=24

Solution for (D^2-5D+6)y=24 equation:

(^2-5+6)D=24

We move all terms to the left:

(^2-5+6)D-(24)=0

We multiply parentheses

D^2-5D+6D-24=0

We add all the numbers together, and all the variables

D^2+D-24=0

a = 1; b = 1; c = -24;
Δ = b2-4ac
Δ = 12-4·1·(-24)
Δ = 97
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{-(1)-\sqrt{97}}{2*1}=\frac{-1-\sqrt{97}}{2}
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*1}=\frac{-1+\sqrt{97}}{2}
$