n-2(180)/n=170

Solution for n-2(180)/n=170 equation:

n-2(180)/n=170

We move all terms to the left:

n-2(180)/n-(170)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


n*n-170*n-2180=0

We add all the numbers together, and all the variables

-170n+n*n-2180=0

Wy multiply elements

n^2-170n-2180=0

a = 1; b = -170; c = -2180;
Δ = b2-4ac
Δ = -1702-4·1·(-2180)
Δ = 37620
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:

$\sqrt{\Delta}=\sqrt{37620}=\sqrt{36*1045}=\sqrt{36}*\sqrt{1045}=6\sqrt{1045}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-170)-6\sqrt{1045}}{2*1}=\frac{170-6\sqrt{1045}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-170)+6\sqrt{1045}}{2*1}=\frac{170+6\sqrt{1045}}{2}
$