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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1D+(^2-7+12)D=0

We multiply parentheses

D^2-1D-7D+12D=0

We add all the numbers together, and all the variables

D^2+4D=0

a = 1; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·1·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*1}=\frac{-8}{2}
=-4
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*1}=\frac{0}{2}
=0
$