1/2p=21-p

Solution for 1/2p=21-p equation:

1/2p=21-p

We move all terms to the left:

1/2p-(21-p)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

1/2p-(-1p+21)=0

We get rid of parentheses

1/2p+1p-21=0

We multiply all the terms by the denominator


1p*2p-21*2p+1=0

Wy multiply elements

2p^2-42p+1=0

a = 2; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·2·1
Δ = 1756
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:

$\sqrt{\Delta}=\sqrt{1756}=\sqrt{4*439}=\sqrt{4}*\sqrt{439}=2\sqrt{439}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{439}}{2*2}=\frac{42-2\sqrt{439}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{439}}{2*2}=\frac{42+2\sqrt{439}}{4}
$