43/8-115/4p=1/3p

Solution for 43/8-115/4p=1/3p equation:

43/8-115/4p=1/3p

We move all terms to the left:

43/8-115/4p-(1/3p)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

-115/4p-(+1/3p)+43/8=0

We get rid of parentheses

-115/4p-1/3p+43/8=0

We calculate fractions


1548p^2/768p^2+(-22080p)/768p^2+(-256p)/768p^2=0

We multiply all the terms by the denominator


1548p^2+(-22080p)+(-256p)=0

We get rid of parentheses

1548p^2-22080p-256p=0

We add all the numbers together, and all the variables

1548p^2-22336p=0

a = 1548; b = -22336; c = 0;
Δ = b2-4ac
Δ = -223362-4·1548·0
Δ = 498896896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{498896896}=22336$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22336)-22336}{2*1548}=\frac{0}{3096}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22336)+22336}{2*1548}=\frac{44672}{3096}
=14+166/387
$