2p+3-(5p-2)/6p+11=2/17

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Solution for 2p+3-(5p-2)/6p+11=2/17 equation:



2p+3-(5p-2)/6p+11=2/17
We move all terms to the left:
2p+3-(5p-2)/6p+11-(2/17)=0
Domain of the equation: 6p!=0
p!=0/6
p!=0
p∈R
We add all the numbers together, and all the variables
2p-(5p-2)/6p+3+11-(+2/17)=0
We add all the numbers together, and all the variables
2p-(5p-2)/6p+14-(+2/17)=0
We get rid of parentheses
2p-(5p-2)/6p+14-2/17=0
We calculate fractions
2p+(-85p+34)/102p+(-12p)/102p+14=0
We multiply all the terms by the denominator
2p*102p+(-85p+34)+(-12p)+14*102p=0
Wy multiply elements
204p^2+(-85p+34)+(-12p)+1428p=0
We get rid of parentheses
204p^2-85p-12p+1428p+34=0
We add all the numbers together, and all the variables
204p^2+1331p+34=0
a = 204; b = 1331; c = +34;
Δ = b2-4ac
Δ = 13312-4·204·34
Δ = 1743817
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{-(1331)-\sqrt{1743817}}{2*204}=\frac{-1331-\sqrt{1743817}}{408} $
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1331)+\sqrt{1743817}}{2*204}=\frac{-1331+\sqrt{1743817}}{408} $

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