(D^2-9D-52)y=0

Solution for (D^2-9D-52)y=0 equation:

(^2-9-52)D=0

We multiply parentheses

D^2-9D-52D=0

We add all the numbers together, and all the variables

D^2-61D=0

a = 1; b = -61; c = 0;
Δ = b2-4ac
Δ = -612-4·1·0
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-61}{2*1}=\frac{0}{2}
=0
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+61}{2*1}=\frac{122}{2}
=61
$