p/3p+16=46+2p

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Solution for p/3p+16=46+2p equation:



p/3p+16=46+2p
We move all terms to the left:
p/3p+16-(46+2p)=0
Domain of the equation: 3p!=0
p!=0/3
p!=0
p∈R
We add all the numbers together, and all the variables
p/3p-(2p+46)+16=0
We get rid of parentheses
p/3p-2p-46+16=0
We multiply all the terms by the denominator
p-2p*3p-46*3p+16*3p=0
Wy multiply elements
-6p^2+p-138p+48p=0
We add all the numbers together, and all the variables
-6p^2-89p=0
a = -6; b = -89; c = 0;
Δ = b2-4ac
Δ = -892-4·(-6)·0
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-89}{2*-6}=\frac{0}{-12} =0 $
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+89}{2*-6}=\frac{178}{-12} =-14+5/6 $

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