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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


2p+(-55p+22)/66p+(-12p)/66p+3+11=0

We add all the numbers together, and all the variables

2p+(-55p+22)/66p+(-12p)/66p+14=0

We multiply all the terms by the denominator


2p*66p+(-55p+22)+(-12p)+14*66p=0

Wy multiply elements

132p^2+(-55p+22)+(-12p)+924p=0

We get rid of parentheses

132p^2-55p-12p+924p+22=0

We add all the numbers together, and all the variables

132p^2+857p+22=0

a = 132; b = 857; c = +22;
Δ = b2-4ac
Δ = 8572-4·132·22
Δ = 722833
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{-(857)-\sqrt{722833}}{2*132}=\frac{-857-\sqrt{722833}}{264}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(857)+\sqrt{722833}}{2*132}=\frac{-857+\sqrt{722833}}{264}
$