2p+1/2p=45

Solution for 2p+1/2p=45 equation:

2p+1/2p=45

We move all terms to the left:

2p+1/2p-(45)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We multiply all the terms by the denominator


2p*2p-45*2p+1=0

Wy multiply elements

4p^2-90p+1=0

a = 4; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·4·1
Δ = 8084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8084}=\sqrt{4*2021}=\sqrt{4}*\sqrt{2021}=2\sqrt{2021}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2021}}{2*4}=\frac{90-2\sqrt{2021}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2021}}{2*4}=\frac{90+2\sqrt{2021}}{8}
$