1/2p+2/p+3/p=1

Solution for 1/2p+2/p+3/p=1 equation:

1/2p+2/p+3/p=1

We move all terms to the left:

1/2p+2/p+3/p-(1)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: p!=0

p∈R


We calculate fractions


p/2p^2+(6p+2)/2p^2-1=0

We multiply all the terms by the denominator


p+(6p+2)-1*2p^2=0

Wy multiply elements

-2p^2+p+(6p+2)=0

We get rid of parentheses

-2p^2+p+6p+2=0

We add all the numbers together, and all the variables

-2p^2+7p+2=0

a = -2; b = 7; c = +2;
Δ = b2-4ac
Δ = 72-4·(-2)·2
Δ = 65
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{-(7)-\sqrt{65}}{2*-2}=\frac{-7-\sqrt{65}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{65}}{2*-2}=\frac{-7+\sqrt{65}}{-4}
$