4/5n=180n-360

Solution for 4/5n=180n-360 equation:

4/5n=180n-360

We move all terms to the left:

4/5n-(180n-360)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We get rid of parentheses

4/5n-180n+360=0

We multiply all the terms by the denominator


-180n*5n+360*5n+4=0

Wy multiply elements

-900n^2+1800n+4=0

a = -900; b = 1800; c = +4;
Δ = b2-4ac
Δ = 18002-4·(-900)·4
Δ = 3254400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3254400}=\sqrt{14400*226}=\sqrt{14400}*\sqrt{226}=120\sqrt{226}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1800)-120\sqrt{226}}{2*-900}=\frac{-1800-120\sqrt{226}}{-1800}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1800)+120\sqrt{226}}{2*-900}=\frac{-1800+120\sqrt{226}}{-1800}
$