2/3p-3/5p=8

Solution for 2/3p-3/5p=8 equation:

2/3p-3/5p=8

We move all terms to the left:

2/3p-3/5p-(8)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We calculate fractions


10p/15p^2+(-9p)/15p^2-8=0

We multiply all the terms by the denominator


10p+(-9p)-8*15p^2=0

Wy multiply elements

-120p^2+10p+(-9p)=0

We get rid of parentheses

-120p^2+10p-9p=0

We add all the numbers together, and all the variables

-120p^2+p=0

a = -120; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-120)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-120}=\frac{-2}{-240}
=1/120
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-120}=\frac{0}{-240}
=0
$