1/4p=16-1/3p

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Solution for 1/4p=16-1/3p equation:



1/4p=16-1/3p
We move all terms to the left:
1/4p-(16-1/3p)=0
Domain of the equation: 4p!=0
p!=0/4
p!=0
p∈R
Domain of the equation: 3p)!=0
p!=0/1
p!=0
p∈R
We add all the numbers together, and all the variables
1/4p-(-1/3p+16)=0
We get rid of parentheses
1/4p+1/3p-16=0
We calculate fractions
3p/12p^2+4p/12p^2-16=0
We multiply all the terms by the denominator
3p+4p-16*12p^2=0
We add all the numbers together, and all the variables
7p-16*12p^2=0
Wy multiply elements
-192p^2+7p=0
a = -192; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-192)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-192}=\frac{-14}{-384} =7/192 $
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-192}=\frac{0}{-384} =0 $

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