4/p+2=5/6p

Solution for 4/p+2=5/6p equation:

4/p+2=5/6p

We move all terms to the left:

4/p+2-(5/6p)=0


Domain of the equation: p!=0

p∈R



Domain of the equation: 6p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

4/p-(+5/6p)+2=0

We get rid of parentheses

4/p-5/6p+2=0

We calculate fractions


24p/6p^2+(-5p)/6p^2+2=0

We multiply all the terms by the denominator


24p+(-5p)+2*6p^2=0

Wy multiply elements

12p^2+24p+(-5p)=0

We get rid of parentheses

12p^2+24p-5p=0

We add all the numbers together, and all the variables

12p^2+19p=0

a = 12; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·12·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*12}=\frac{-38}{24}
=-1+7/12
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*12}=\frac{0}{24}
=0
$