2p+1/p=5

Solution for 2p+1/p=5 equation:

2p+1/p=5

We move all terms to the left:

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


Domain of the equation: p!=0

p∈R


We multiply all the terms by the denominator


2p*p-5*p+1=0

We add all the numbers together, and all the variables

-5p+2p*p+1=0

Wy multiply elements

2p^2-5p+1=0

a = 2; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·2·1
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{17}}{2*2}=\frac{5-\sqrt{17}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{17}}{2*2}=\frac{5+\sqrt{17}}{4}
$