1/3p-5/6=2+1/4p

Solution for 1/3p-5/6=2+1/4p equation:

1/3p-5/6=2+1/4p

We move all terms to the left:

1/3p-5/6-(2+1/4p)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 4p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

1/3p-(1/4p+2)-5/6=0

We get rid of parentheses

1/3p-1/4p-2-5/6=0

We calculate fractions


(-240p^2)/432p^2+144p/432p^2+(-108p)/432p^2-2=0

We multiply all the terms by the denominator


(-240p^2)+144p+(-108p)-2*432p^2=0

Wy multiply elements

(-240p^2)-864p^2+144p+(-108p)=0

We get rid of parentheses

-240p^2-864p^2+144p-108p=0

We add all the numbers together, and all the variables

-1104p^2+36p=0

a = -1104; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-1104)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-1104}=\frac{-72}{-2208}
=3/92
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-1104}=\frac{0}{-2208}
=0
$