(2p+3)-(5p-2)/6p=11=2/7

Solution for (2p+3)-(5p-2)/6p=11=2/7 equation:

(2p+3)-(5p-2)/6p=11=2/7

We move all terms to the left:

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


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

12p^2-(5p-2)+18p-66p=0

We get rid of parentheses

12p^2-5p+18p-66p+2=0

We add all the numbers together, and all the variables

12p^2-53p+2=0

a = 12; b = -53; c = +2;
Δ = b2-4ac
Δ = -532-4·12·2
Δ = 2713
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{-(-53)-\sqrt{2713}}{2*12}=\frac{53-\sqrt{2713}}{24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{2713}}{2*12}=\frac{53+\sqrt{2713}}{24}
$