-41=-(2/5)(45n+60)+n

Solution for -41=-(2/5)(45n+60)+n equation:

-41=-(2/5)(45n+60)+n

We move all terms to the left:

-41-(-(2/5)(45n+60)+n)=0


Domain of the equation: 5)(45n+60)+n)!=0

n∈R


We add all the numbers together, and all the variables

-(-(+2/5)(45n+60)+n)-41=0

We multiply parentheses ..

-(-(+90n^2+2/5*60)+n)-41=0

We multiply all the terms by the denominator


-(-(+90n^2+2-41*5*60)+n)=0


We calculate terms in parentheses: -(-(+90n^2+2-41*5*60)+n), so:

-(+90n^2+2-41*5*60)+n

We get rid of parentheses

-90n^2+n-2+41*5*60

We add all the numbers together, and all the variables

-90n^2+n+12298

Back to the equation:

-(-90n^2+n+12298)


We get rid of parentheses

90n^2-n-12298=0

We add all the numbers together, and all the variables

90n^2-1n-12298=0

a = 90; b = -1; c = -12298;
Δ = b2-4ac
Δ = -12-4·90·(-12298)
Δ = 4427281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{4427281}}{2*90}=\frac{1-\sqrt{4427281}}{180}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{4427281}}{2*90}=\frac{1+\sqrt{4427281}}{180}
$