(D^3+160)y=0

Solution for (D^3+160)y=0 equation:

(^3+160)D=0

We multiply parentheses

D^2+160D=0

a = 1; b = 160; c = 0;
Δ = b2-4ac
Δ = 1602-4·1·0
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-160}{2*1}=\frac{-320}{2}
=-160
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+160}{2*1}=\frac{0}{2}
=0
$