1/2p=1/4p+1

Solution for 1/2p=1/4p+1 equation:

1/2p=1/4p+1

We move all terms to the left:

1/2p-(1/4p+1)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 4p+1)!=0

p∈R


We get rid of parentheses

1/2p-1/4p-1=0

We calculate fractions


4p/8p^2+(-2p)/8p^2-1=0

We multiply all the terms by the denominator


4p+(-2p)-1*8p^2=0

Wy multiply elements

-8p^2+4p+(-2p)=0

We get rid of parentheses

-8p^2+4p-2p=0

We add all the numbers together, and all the variables

-8p^2+2p=0

a = -8; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-8)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-8}=\frac{-4}{-16}
=1/4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-8}=\frac{0}{-16}
=0
$