(D^2+D-6)y=X

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

(^2+-6)D=D

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1D+(^2+-6)D=0

We use the square of the difference formula

-1D+(^2-6)D=0

We multiply parentheses

D^2-1D-6D=0

We add all the numbers together, and all the variables

D^2-7D=0

a = 1; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·1·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*1}=\frac{0}{2}
=0
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*1}=\frac{14}{2}
=7
$