n+2/n-1=5n

Solution for n+2/n-1=5n equation:

n+2/n-1=5n

We move all terms to the left:

n+2/n-1-(5n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-4n+2/n-1=0

We multiply all the terms by the denominator


-4n*n-1*n+2=0

We add all the numbers together, and all the variables

-1n-4n*n+2=0

Wy multiply elements

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

a = -4; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-4)·2
Δ = 33
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{33}}{2*-4}=\frac{1-\sqrt{33}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*-4}=\frac{1+\sqrt{33}}{-8}
$