2p+1/2p=25

Solution for 2p+1/2p=25 equation:

2p+1/2p=25

We move all terms to the left:

2p+1/2p-(25)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We multiply all the terms by the denominator


2p*2p-25*2p+1=0

Wy multiply elements

4p^2-50p+1=0

a = 4; b = -50; c = +1;
Δ = b2-4ac
Δ = -502-4·4·1
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-6\sqrt{69}}{2*4}=\frac{50-6\sqrt{69}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+6\sqrt{69}}{2*4}=\frac{50+6\sqrt{69}}{8}
$