360n=-200n^2-144

Solution for 360n=-200n^2-144 equation:

360n=-200n^2-144

We move all terms to the left:

360n-(-200n^2-144)=0

We get rid of parentheses

200n^2+360n+144=0

a = 200; b = 360; c = +144;
Δ = b2-4ac
Δ = 3602-4·200·144
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-120}{2*200}=\frac{-480}{400}
=-1+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+120}{2*200}=\frac{-240}{400}
=-3/5
$