P=2n-1/n+1

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

=2P-1/P+1

We move all terms to the left:

-(2P-1/P+1)=0


Domain of the equation: P+1)!=0

P∈R


We get rid of parentheses

-2P+1/P-1=0

We multiply all the terms by the denominator


-2P*P-1*P+1=0

We add all the numbers together, and all the variables

-1P-2P*P+1=0

Wy multiply elements

-2P^2-1P+1=0

a = -2; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-2)·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*-2}=\frac{-2}{-4}
=1/2
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*-2}=\frac{4}{-4}
=-1
$