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

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+3)-(5p-2)/6p+11-(+2/17)=0

We get rid of parentheses

2p-(5p-2)/6p+3+11-2/17=0

We calculate fractions


2p+(-85p+34)/102p+(-12p)/102p+3+11=0

We add all the numbers together, and all the variables

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}
$