3p+p=1/2p=18

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Solution for 3p+p=1/2p=18 equation:



3p+p=1/2p=18
We move all terms to the left:
3p+p-(1/2p)=0
Domain of the equation: 2p)!=0
p!=0/1
p!=0
p∈R
We add all the numbers together, and all the variables
3p+p-(+1/2p)=0
We add all the numbers together, and all the variables
4p-(+1/2p)=0
We get rid of parentheses
4p-1/2p=0
We multiply all the terms by the denominator
4p*2p-1=0
Wy multiply elements
8p^2-1=0
a = 8; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·8·(-1)
Δ = 32
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:
$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2}}{2*8}=\frac{0-4\sqrt{2}}{16} =-\frac{4\sqrt{2}}{16} =-\frac{\sqrt{2}}{4} $
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*8}=\frac{0+4\sqrt{2}}{16} =\frac{4\sqrt{2}}{16} =\frac{\sqrt{2}}{4} $

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