(-5n-1)/(n+3)n=4

Solution for (-5n-1)/(n+3)n=4 equation:

(-5n-1)/(n+3)n=4

We move all terms to the left:

(-5n-1)/(n+3)n-(4)=0


Domain of the equation: (n+3)n!=0

n∈R


We multiply all the terms by the denominator


(-5n-1)-4*(n+3)n=0

We multiply parentheses

-4n^2+(-5n-1)-12n=0

We get rid of parentheses

-4n^2-5n-12n-1=0

We add all the numbers together, and all the variables

-4n^2-17n-1=0

a = -4; b = -17; c = -1;
Δ = b2-4ac
Δ = -172-4·(-4)·(-1)
Δ = 273
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{-(-17)-\sqrt{273}}{2*-4}=\frac{17-\sqrt{273}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{273}}{2*-4}=\frac{17+\sqrt{273}}{-8}
$